See what the Smithsonian has to say about Chechnya's history.

PD The Atlas of Ancient and Classical Geography by Samuel Butler, Ernest Rhys, ed. (1907, 1908) Alt: Armenia, Colchis, Iberia, Albania.
In history, Chechnya has straddled the areas we call Europe and Asia. [See: Ancient Asia from the Perspective of Ancient Greece and Rome.] It was one of the areas over which that remarkably resilient thorn in Rome's side, known as the Poison King (Mithradates of Pontus), held sway. In Greek mythology, this is the general vicinity of Medea and Jason's quest for the Golden Fleece, which involved a dangerous sea voyage to the scarcely known regions of the ancient world.
It appears that the Cimmerians, a Steppe people, are among the many groups who invaded the area. Herodotus discusses the Cimmerians in the fourth book of his histories.
The geographer Strabo (c. 64 B.C. - c. A.D. 21) describes a group of people believed to have lived in the area before the Cimmerians. These are the Zygi. Here is an extended translated passage from Strabo (from Lacus Curtius) about the area. The Zygi are highlighted:
Book XI, Chapter 15 As we pass from Europe to Asia in our geography, the northern division is the first of the two divisions to which we come; and therefore we must begin with this. Of this division the first portion is that in the region of the Tanaïs River, which I have taken as the boundary between Europe and Asia. This portion forms, in a way, a peninsula, for it is surrounded on the west by the Tanaïs River and Lake Maeotis as far as the Bosporus and that part of the coast of the Euxine Sea which terminates at Colchis [See map]; and then on the north by the Ocean as far as the mouth of the Caspian Sea; and then on the east by this same sea as far as the boundary between Albania and Armenia, where empty the rivers Cyrus and Araxes, the Araxes flowing through Armenia and the Cyrus through Iberia and Albania; and lastly, on the south by the tract of country which extends from the outlet of the Cyrus River to Colchis, which is about three thousand stadia from sea to sea, across the territory of the Albanians and the Iberians, and therefore is described as an isthmus. But those writers who have reduced the width of the isthmus as much as Cleitarchus has, who says that it is subject to inundation from either sea, should not be considered even worthy of mention. Poseidonius states that the isthmus is fifteen hundred stadia across, as wide as the isthmus from Pelusium to the Red Sea. "And in my opinion," he says, "the isthmus from Lake Maeotis to the Ocean does not differ much therefrom."
6 But I do not know how anyone can trust him concerning things that are uncertain if he has nothing plausible to say about them, when he reasons so illogically about things that are obvious; and this too, although he was a friend of Pompey, who made an expedition against the Iberians and the Albanians, from sea to sea on either side, both the Caspian and the Colchian Seas. At any rate, it is said that Pompey, upon arriving at Rhodes on his expedition against the pirates (immediately thereafter he was to set out against both Mithridates and the tribes which extended as far as the Caspian Sea), happened to attend one of the lectures of Poseidonius, and that when he went out he asked Poseidonius whether he had any orders to give, and that Poseidonius replied: "Ever bravest be, and pre‑eminent o'er others." Add to this that among other works he wrote also the history of Pompey. So for this reason he should have been more regardful of the truth.
7 The second portion would be that beyond the Hyrcanian Sea, which we call the Caspian Sea, as far as the Scythians near India. The third portion would consist of the part which is adjacent to the isthmus above mentioned and of those parts of the region inside Taurus and nearest Europe which come next after this isthmus and the Caspian Gates, I mean Media and Armenia and Cappadocia and the intervening regions. The fourth portion is the land inside the Halys River, and all the region in the Taurus itself and outside thereof which falls within the limits of the peninsula which is formed by the isthmus that separates the Pontic and the Cilician Seas. As for the other countries, I mean the Trans-Tauran, I place among them not only India, but also Ariana as far as the tribes that extend to the Persian Sea and the Arabian Gulf and the Nile and the Egyptian and Issic Seas.
Book XI, Chapter 2
1 Of the portions thus divided, the first is inhabited, in the region toward the north and the Ocean, by Scythian nomads and waggon-dwellers, and south of these, by Sarmatians, these too being Scythians, and by Aorsi and Siraci, who extend towards the south as far as the Caucasian Mountains, some being nomads and others tent-dwellers and farmers. About Lake Maeotis live the Maeotae. And on the sea lies the Asiatic side of the Bosporus, or the Sindic [Indian] territory. After this latter, one comes to the Achaei and the Zygi and the Heniochi, and also the Cercetae and the Macropogones. And above these are situated the narrow passes of the Phtheirophagi; and after the Heniochi the Colchian country, which lies at the foot of the Caucasian, or Moschian, Mountains. But since I have taken the Tanaïs River as the boundary between Europe and Asia, I shall begin my detailed description therewith.
Relateds:
As I learn more about the ancient residents of this area of the world, I will post. If you have reliable sources on the ancient history of the modern political region, please post in the comments. If you have an online map showing the Eurasian dividing lines Strabo uses, please post a link to it.

Comments
Chechnya, in my opinion, probably was the home of the Kaska, enemies of the Hittites. They spoke a language of the Altaic group- as was Sumerian, Basque, and Turkish. North America, as well, received this group when the Athabaskans emigrated there beginning about 1,000 BCE.
The question then becomes whether the Cimmerians were Kaska or Iranian nomads and thus Indo-European. Since the nomadic predecessors of the Cimmerians were the Szygi (Strabo), I would suppose these to be “Kaska” and doubtlessly wherefrom the very term “Scythian” comes.
I suspect the Cimmerians to have been a dialectical opposite to the Scythians and to have included the Dacians and Thracians. Thus, they would have been “post-Hittite” (Lydian, Lycian, Phrygian, etc.). The Scythians probably were a duality of Kaska and the Iranian Ossetians (in the Caucasus). Circassians there probably are Kaska, as well. Sarmatians , then, were presumably more of a technical development in this military dialectic- their armor versus Scythian archery.
The Indo-European Age ended when first the Tocharians (Kelts) and then the Iranian Alans, Saka, Sarmatians, and Germanic Goths were rolled back by the Huns, Avars, and Turks, especially after 300 BCE. Thus, the dialectical ebb and flow of race in Eurasia’s steppe…
A clarification:
Dialectic, a term used by Marx, tended to mean class against class. Here, l mean it militarily and technically. The Hittites used chariots but the Cimmerians simply rode their horses. The Scythians became mounted pastoralists. The Huns may have been first to develop stirrups upon which they could draw their compound bows (of different materials: wood; bone; sinew).
But a broader dialectic also emerges: that of race. The Indo-Europeans must have formed when they, as Finnics, encountered Altaics (Basques, etc.) at about 6000 BCE. The Pontic Indo-Europeans then struggled with the Caucasus Altaics for control of Asia Minor and then of the Steppe. From this emerged potent tribes such as Tartars and Mongols. These drove Indo-Europeans from the Steppe but they also saved medieval Europe from the Turks and indirectly protected its Rennaisance. Without them, we’d be under the Crescent for better or worse…
Indeed, the first steppe cavalrists must have been the ancients we now know as the Dacians and Thracians. These had a National Geography article about them a few years ago. If they were first named the “Szigy”, then perhaps this led to that of the “Scythians”. But I will name them the “Proto-Scythians”. They were then driven from the Steppe by the Cimmerians. This may also have resulted in some of the nations of Asia Minor- the Phrygians, for example.
The Kelts had preceded the proto-Scythians, so I wonder if those weren’t derived from interactions with Caucasian tribes such as Chechnyans. Ultimately, Finnics must have interacted with Caucasians to form “Pontic”, the first Indo-European because languages developed as interactions between two different groups. Hittite probably developed as an interaction with Etruscan in Asia Minor at the same time Scythian formed. Keltic must have been the same as the original Pontic which then changed as they spread out from Ireland to Mongolia and from Scandanavia to India…