Linear and nonlinear gyrokinetic simulations of collisionless magnetic reconnection in the presence of a strong guide field are presented. A periodic slab system is considered with a sinusoidally varying reconnecting magnetic field component. The linear growth rates of the tearing mode in both the large and small Delta(') regimes are compared to kinetic and fluid theory calculations. In the nonlinear regime, focusing on the limit of large Delta('), the nonlinear reconnection rates in the gyrokinetic simulations are found to be comparable to those obtained from a two-fluid model. In contrast to the fluid system, however, for T-i > T-e and very small initial perturbation amplitudes, the reconnection in the gyrokinetic system saturates in the early nonlinear phase. This saturation can be overcome if the simulation is seeded initially with sufficient random noise.