In this paper, we are concerned with chirped solitary wave solutions in negative indexed materials having Kerr nonlinearity and self-phase modulation term. An auxiliary equation method together with an ansatz technique are employed. New chirped dark solitons, bright solitons, and trigonometric map solutions by using the auxiliary equation technique are obtained. Both 2- and 3-dimensional graphs are provided to illustrate the obtained results. The presented research will be useful especially for scientists who are studying solitons.