The presence of bias in measurement of rate gyros is a performance limiting factor for satellite attitude determination systems. Gyro bias is usually handled by Kalman filtering methods which are mostly based on linearization approaches and lack global convergence properties. On the other hand, the existing asymptotically convergent nonlinear observers take into account the gyro bias only when multiple vector measurements are available. We present an asymptotically convergent attitude estimator which uses only one vector measurement and a rate gyro whose output is contaminated with an unknown and constant bias. The effect of unknown bias is compensated by means of a parameter adaptation law. An explicit condition on the reference vectors for ensuring observability of the system is introduced. A realistic simulation is presented to illustrate the performance of the proposed attitude estimator in face of significant bias in gyro measurement and when a magnetometer is used to provide the single vector measurement.