In generative syntax, a chain composition is a process by which two independent chains, say (a1,...,an) and (b1,...,bn), are linked to each other, thus forming one extended chain (a1,...,an,b1,...,bn).
Chain composition presumably takes place in a.o. parasitic gap constructions. Thus, in (i) there are two chains, (which gapsi , ti ), the result of wh-movement in the matrix clause, and (Opj, tj), resulting from movement of the empty Operator in the embedded adjunct clause. To give the parasitic gap in the embedded clause its correct interpretation (i.e. as a variable bound by which gaps), the chain headed by the Operator must be composed with the chain headed by which gaps.
(i) which gapsi did you hate ti [before [Opj [analyzing tj ]]]
The locality restriction on Chain composition (an and b1 may not be too far apart) has been formulated in terms of Subjacency.