The problem of distributed multiuser medium access of a hierarchical cognitive radio network with multiple primary and secondary users is considered. Each primary user has a licensed channel; it allows access by secondary cognitive users under certain collision constraints. The secondary cognitive users seek to capture transmission opportunities while avoiding collisions with primary and other secondary users. Under tight collision constraints, we establish the maximum throughput region achievable by distributed multiaccess of secondary users when the number of secondary users is less than the number of primary channels using a scheme referred to as the Distributed Orthogonal and Periodic Sensing with Memoryless Access (DOPS-MA). Packet-level simulations are used to validate the performance prediction.