We study a flexible algorithm for minimizing a sum of component functions, each of which depends on a large number of decision variables. The algorithm combines aspects of incremental gradient method with that of coordinate descent. In contrast to earlier algorithms of this kind, our algorithm is lock-free and does not require synchronization of access to the shared memory. We prove convergence of the algorithm under asynchronous operation and provide explicit bounds on how the solution times depend on the degree of asynchrony. Numerical experiments confirm our theoretical results.