We study a distributed algorithm for adapting transmit beamforming vectors in a multi-antenna peer-to-peer wireless network. The algorithm attempts to maximize a sum of per-user utility functions, where each user's utility is a function of his transmission rate, or equivalently the received signal-to-interference plus noise ratio (SINR). This is accomplished by exchanging interference prices, each of which represents the marginal cost of interference to a particular user. Given the interference prices, users update their beamforming vectors to maximize their utility minus the cost of interference. For a two-user system, we show that this algorithm converges for a suitable class of utility functions. Convergence of the algorithm with more than two users is illustrated numerically.