  Using the minimal parameter sequence of a given chain sequence, we introduce
the concept of complementary chain sequences, which we view as perturbations of
chain sequences. Using the relation between these complementary chain sequences
and the corresponding Verblunsky coefficients, the para-orthogonal polynomials
and the associated Szeg\"o polynomials are analyzed. Two illustrations, one
involving Gaussian hypergeometric functions and the other involving
Carath\'eodory functions are also provided. A connection between these two
illustrations by means of complementary chain sequences is also observed.
