The control of a linear stochastic system with a Brownian motion and a cost functional that is quadratic in the state and the control (linear-quadratic Gaussian control) is probably the most well known continuous time, solvable stochastic control problem.  The family of standard fractional Brownian motions is indexed by the Hurst parameter, H in (0, 1).  If H = ?then the process is a standard Brownian motion.  If H is not ?then the Gaussian process is neither a semimartingale nor a Markov process.   Empirical evidence suggests that other members of the family of fractional Brownian motions are more appropriate for modeling noise in a physical system.  In this talk a stochastic control problem for a linear stochastic system with an arbitrary fractional Brownian motion and a cost functional that is quadratic in the state and the control is formulated and explicitly solved.  The optimal control is a sum of two terms, one term is the well known linear feedback term for the case of Brownian motion or the associated deterministic control problem and the other term is the minimum mean square error prediction of the response of the optimal system to the future fractional Brownian motion.