1. <operating system> (From BASIC's "CHAIN" statement) To pass control to a child or successor without going through the operating system command interpreter that invoked you. The state of the parent program is lost and there is no returning to it. Though this facility used to be common on memory-limited microcomputers and is still widely supported for backward compatibility, the jargon usage is semi-obsolescent; in particular, Unix calls this exec.
Compare with the more modern "subshell".
2. <programming> A series of linked data areas within an operating system or application program. "Chain rattling" is the process of repeatedly running through the linked data areas searching for one which is of interest. The implication is that there are many links in the chain.
3. <theory> A possibly infinite, non-decreasing sequence of elements of some total ordering, S
x0 <= x1 <= x2 ...
A chain satisfies:
for all x,y in S, x <= y / y <= x.
I.e. any two elements of a chain are related.
("<=" is written in LaTeX as sqsubseteq).