Carrier-Sense Multiple Access with Transmission Acquisition (CSMA/TA) and channel-access prioritization is presented. CSMA/TA is intended for wireless local area networks of stations endowed with half-duplex transceivers and single antennas. It leverages the small turnaround times of current half-duplex radios to increase the likelihood of having the last transmission from a group of overlapping transmissions succeed, especially if turnaround times are smaller or slightly larger than propagation delays. In CSMA/TA, a station senses the channel before sending a pilot and waits for a short time after sending its pilot before sensing the channel again. If the channel is sensed idle again, the station transmits its data packet. By using appropriate pilot lengths, CSMA/TA allows traffic prioritization at the channel-access level, which supplements traditional output traffic prioritization at stations. It is shown that non-priority CSMA/TA can surpass the performance of such protocols as CSMA, FAMA-PJ, and CSMA/CD if turnaround times are larger than propagation delays, but not too much larger. In addition, it is shown that CSMA/TA can improve traffic prioritization significantly across different traffic classes, under different traffic load proportions, compared to CSMA under the same conditions.