Clonal cell culture is crucial for experimental protocols that require growth or selection of pure populations of cells. High-density derivation of neural progenitors from human embryonic stem cells (hESCs) can lead to incomplete differentiation, and transplantation of resulting heterogeneous cell mixtures can cause proliferation of tumorigenic clusters in vivo. We have identified the neural precursor that resides among normal hESC colonies as a TRA-1-60(-)/SSEA4(-)/SOX1(+) cell and developed a method that allows for the clonal expansion of these FACS-selected progenitors to neural stem cells (NSCs) in serum-free conditions. Single TRA-1-60(-)/SSEA4(-)/SOX1(+) cells grown in serum-free media give rise to multipotent NSCs with an efficiency of 0.7%. The fate of the TRA-1-60(-)/SSEA4(-)/SOX1(+) neural precursor becomes specified in maintenance conditions by inhibition of BMP signaling. This clonal culture method can be scaled up to produce NSCs for differentiation and use in cell therapies.