The IEEE 802.15.4 standard defines the medium access control (MAC) and physical layer for sensor networks. One of the MAC schemes proposed is slotted Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), and this paper analyzes whether this scheme meets the design constraints of low-power and low-cost sensor networks. The paper provides a detailed analytical evaluation of its performance in a star topology network for both saturated and unsaturated periodic traffic. The form of the analysis is similar to that of Bianchi for IEEE 802.11 DCF only in the use of a per user Markov model to capture the state of each user at each moment in time. The key assumptions to enable this important simplification and the coupling of the per user Markov models are however different, as a result of the very different designs of the 802.15.4 and 802.11 carrier sensing mechanisms. The performance predicted by the analytical model is very close to that obtained by simulation. Throughput and energy consumption analysis is then performed and design guidelines are derived.