Abstract: This paper discusses the adaptive control of a linear time-invariant plant when the measurement of the plant output is corrupted by a bounded stochastic noise. The principal contribution is the demonstration of the boundedness of all the signals of the overall system using a new kind of hybrid adaptive law. A statement of the prior information needed to determine the adaptive law is given. Computer simulation is presented to demonstrate the performance of the new adaptive law and to illustrate the effect of various parameters.