Using the Precision Time Protocol (PTP) specified by the IEEE 1588 standard, synchronization of distributed clocks is achieved by propagating the timing information of a preselected master clock throughout the entire network. Based on this directly or indirectly obtained noisy timing information, each slave clock tries to follow as closely as possible the master time. This paper formulates the PTP based clock synchronization as an estimation-control problem. An LQG controller is designed which produces an optimal reconstruction of the master time at each slave in the sense of minimizing the mean square error of the estimator and minimizing an LQR cost function for the controller. The performance of the proposed optimal controller is verified by simulation results.