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This paper considers the problem of observer-based adaptive neural network (NN) control for a class of single-input single-output strict-feedback nonlinear stochastic systems with unknown time delays. Dynamic surface control is used to avoid the so-called explosion of complexity in the backstepping design process. Radial basis function NNs are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions. The proposed adaptive NN output feedback controller can guarantee all the signals in the closed-loop system to be mean square semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the proposed methods.