Atomistic simulations of dislocation mobility reveal that body-centered cubic (BCC) high-entropy alloys (HEAs) are distinctly different from traditional BCC metals. HEAs are concentrated solutions in which composition fluctuation is almost inevitable. The resultant inhomogeneities, while locally promoting kink nucleation on screw dislocations, trap them against propagation with an appreciable energy barrier, replacing kink nucleation as the rate-limiting mechanism. Edge dislocations encounter a similar activated process of nanoscale segment detrapping, with comparable activation barrier. As a result, the mobility of edge dislocations, and hence their contribution to strength, becomes comparable to screw dislocations.