This talk is about the existence of quasi-periodic standing waves in 1D, cubic nonlinear Schr¨odinger equation with a periodic potential. It will be shown that there is a two-frequency quasi-periodic standing wave corresponding to each internal frequency of constant type which is larger than an explicitly given bound. This work, joint with S.N. Chow, M. van Noort and M. A. Porter, is motivated by the study of BECs when considering only two body, mean field interactions in a dilute Bose-Einstein gas in 1D regime.