In wireless ad hoc networks, the major quality of service (QoS) concern and challenge in the design and analysis of contention-based medium access control (MAC) protocols is to achieve good throughput and access delay performance in the presence of hidden terminals, which are defined as the terminals out of the radio coverage area of an intended transmitter but within that of the receiver. We propose and analyze in this paper a new dual-channel random access protocol, called "Double Sense Multiple Access" (DSMA), for improving QoS support in wireless ad hoc networks. By separating the transmissions of ready-to-send (RTS) and data packets into two time-slotted channels and by introducing a novel double sense mechanism, DSMA completely solves the hidden terminal problem and can guarantee the success transmission of data packets. By taking into account the most complex network scenario in which all transmitters are hidden terminals with respect to each other, key QoS metrics such as throughput, blocking probability and access delay are derived mathematically for the proposed DSMA protocol. These analytical results are verified by extensive computer simulations.