Abarim Publications' online Biblical Greek Dictionary
The noun αλυσις (alusis) means chain, which was mostly a thing to bind prisoners with. As such, this word could also describe a state of bondage, of being figuratively in chains. In the classics, on occasion, this word could describe a woman's ornament.
Our word stems from an ancient Proto-Indo-European root "wel-", meaning to wind (hence words like waltz, helix, vulva, and many more), which suggests that our noun essentially described any kind of wound binding or any kind of loss of freedom, which explains Paul's famous references to his "chain" (Ephesians 6:20, 2 Timothy 1:16). Likewise, the great chain with which the angel was to bind Hades, may very well be a language, a social code of conduct or set of norms, even a computer program or some theory that "binds" the forces of chaos into an ordered global operating system, for all mankind to live by.
Our noun αλυσις (alusis), chain, is used 11 times in the New Testament; see full concordance.
An identical second noun αλυσις (alusis) appears not to be used in the Bible, although the story of the man named Legion (Mark 5:3-4) might contain a play on words, with this second noun in mind. This second noun means distress or anguish, and derives from the verb αλυω (aluo), to be deeply stirred or negatively exited (and which also is not used in the New Testament).
The agent with which the action of this verb αλυω (aluo) is brought about is intense psychological trauma: grief, mad passions, despair, and in the time of the New Testament, this verb had assumed the meaning of to wander or roam aimlessly about, meaning that our noun αλυσις (alusis) had gravitated toward a meaning of bondage by grief, and so an exclusion of normal and unrestricted human congress. The story seems to say that the man named Legion was bound by madness, which was a much stronger chain than any restriction imposed by human convention.