A chiral optical negative-index metamaterial design of doubly periodic construction for the near-infrared spectrum is presented. The chirality is realized by incorporating sub-wavelength planar silver-aluminasilver resonators and arranging them in a left-handed helical (i.e., stair-step) configuration as a wave propagates through the metamaterial. An effective material parameter retrieval procedure is developed for general bi-isotropic metamaterials. A numerical design example is presented and the retrieved effective material parameters exhibiting a negative index of refraction are provided.