The superrigidity theorem of Margulis, see Zimmer [17], classifies finite dimensional representations of lattices in semi-simple Lie groups of real rank strictly larger than 1. It is a fundamental problem to obtain the classification of finite dimensional representations of lattices in rank I semi-simple Lie groups. That this problem will be considerably harder than the previous one is suggested by the existence of continuous families of inequivalent representations or, in other words, the existence of non-trivial deformations. In Johnson-Millson [6] and Kourouniotis [8] such deformations were constructed for certain representations of lattices in SO(n, 1) based on a construction of Thurston called bending. The deformation space of the representation of a lattice F=SO(n, 1) obtained by restricting an inclusion SO(n, 1)-,SO(n+ l, 1) to F is of particular interest. If n > 2 the space of infinitesimal deformations is Hi(F, R "+1) where F acts on R "+1 by the restriction of the standard action of SO(n, 1). The space of infinitesimal deformations is non-zero for the standard arithmetic examples and the main point of the papers cited above was to establish that some of these infinitesimal deformations are integrable (in [6] it is also shown that some are not). In this paper, we study the complex analogue of the above example. We let F be a cocompact torsion free lattice in SU(n, 1) and consider the deformation space of the representation of F obtained by restricting an inclusion SU(n, 1)--*SU(n+I, 1). If n > l the space of infinitesimal deformations is H~(F, R)@H~(F, C,+ 1). In the first summand F acts trivially and the infinitesimal deformations are tangent to the obvious deformations obtained by deforming F in U(n, 1) by a curve of homomorphisms into the center of U(n, 1) (observe that the above inclusion factors as SU(n, 1)~U(n , 1)~SU(n+I, 1)). In the second summand F acts by the restriction of the standard action of SU(n, 1). This summand is non-zero for the standard arithmetic examples,