This paper presents a new method for varying the spindle speed to suppress chatter in machining. The spindle speed is varied in pseudo-random fashion within the bandwidth of the spindle system. Both implementation issues and spindle system responses to such signals are investigated. A new method to analyze the stability of machining systems with varying spindle speed is also introduced. The effectiveness and advantages of the random spindle speed variation in chatter suppression is verified using numerical simulations and experiments.