We construct new 1/2 supersymmetric solutions in D = 3, N = 2, matter coupled, U(1) gauged supergravities and study some of their properties. In the most general case they represent a string superposed with gravitational and Chern-Simons electromagnetic waves. The waves are attached to the string and the solution satisfied an electromagnetic self-duality relation. When the sigma model is non-compact it interpolates between as asymptotically Kaigorodov space and a naked singularity. For the compact sigma model there is a regular horizon with the Kaigorodov geometry and asymptotically it is either Minkowskian or a pp-wave. When the sigma manifold is flat our solutions describe either AdS(3) or Kaigorodov space of a pp-wave in AdS(3).