This paper is concerned with the use of the least squares (LS) algorithm to design a feedback control law to stabilize a basic class of discrete-time nonlinear uncertain systems. The result shows that if a certain polynomial criterion is satisfied, the system can be stabilized by feedback based on the LS algorithm for Gaussian distributed noise and unknown parameters. This result thus provides an answer to the question of what are the fundamental limitations of the discrete-time adaptive nonlinear control. This issue of feedback capability has been an open problem for more than ten years since it was put forward.