The problem of opportunistic access of parallel channels occupied by primary users is considered. Under a continuous-time Markov chain modeling of the channel occupancy by the primary users, a slotted transmission protocol for secondary users using a periodic sensing strategy with optimal dynamic access is proposed. To maximize channel utilization while limiting interference to primary users, a framework of constrained Markov decision processes is presented, and the optimal access policy is derived via a linear program. Simulations are used for performance evaluation. It is demonstrated that periodic sensing yields negligible loss of throughput when the constraint on interference is tight.