Intentional interference constitutes a major threat for communication networks operating over a shared medium where availability is imperative. Jamming attacks are often simple and cheap to implement. Today's jammers can perform physical carrier sensing in order to disrupt communication more efficiently, especially in a network of simple wireless devices such as sensor nodes, which usually operate over a single frequency (or a limited frequency band) and which cannot benefit from the use of spread spectrum or other more advanced technologies. This paper proposes the medium access (MAC) protocol ANTIJAM which is provably robust against a powerful reactive adversary who can jam a (1-ε)-portion of the time steps, where ε is an arbitrary constant. The adversary uses carrier sensing to make informed decisions on when it is most harmful to disrupt communications. Moreover, we allow the adversary to be adaptive and to have complete knowledge of the entire protocol history. Our MAC protocol is able to make efficient use of the nonjammed time periods and achieves a θ(1)- competitive throughput in this harsh scenario, if ε is constant. In addition, ANTIJAM features a low convergence time and has excellent fairness properties in the sense that channel access probabilities among nodes do not differ by more than a small constant factor.