In this paper, we study an l_∞ type of performance for linear switched systems when the switching sequence is a Markov process. We define the notion of the stochastic l_∞ gain and derive an exact expression for computing it. The stochastic l_∞ gain mimics the l_∞ induced norm of the deterministic operators. We further synthesize an optimal controller for minimizing the stochastic l_∞ gain and argue that this problem can be cast as a tractable linear program.