Many fluid flow problems of practical interest-particularly at high Reynolds number-are characterized by small regions of complex and rapidly-varying fluid motion surrounded by larger regions of relatively smooth flow. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. We present in this paper a fractional-step version of Chorin's projection method for incompressible flow, with adaptive mesh refinement, which is second-order accurate in both space and time. Convection terms are handled by a high-resolution upwind method which provides excellent resolution of small-scale features of the flow, while a multilevel iterative scheme efficiently solves the parabolic and elliptic equations associated with viscosity and the projection. Numerical examples demonstrate the performance of the method on two-dimensional problems involving vortex spindown with viscosity and inviscid vortex merger.