I can't believe I missed this before, as it's exactly the kind of thing that gets my pedantic panties in a wad, but Fro is right; "chain migration" is not the correct term for this. Chain migration refers to a different phenomenon that may sometimes overlap what we are talking about here, but doesn't have to. Specifically, it refers to large movements of people from one place to another. For example, large migrations of Irish and Italian immigrants to ethnic enclaves on the Eastern seaboard represent chain migration. Chain migration can even happen within the same country, such as the movement of large southern rural populations to northern cities, or farmers fleeing the dust bowl to California.
And, no, "chain migration" is not found in federal law (or regulation). The technical legal term for what is being discussed here is "Preference allocation for family-sponsored immigrants."
I suspect there was some recent GOP talking point issued that told people to start calling this "chain migration" because it sounds scarier, because up until recently, it wasn't a term you heard, and now it's everywhere. Right here on this forum, for example, before last Thursday, the term had only ever been used once. In the past week, it shows up a couple dozen times.