Microscopic simulations of fracture dissolution are reported, taking account of the explicit topography of the pore space, the transport of reactants and products, and the chemical kinetics at the solid surfaces. A three-dimensional numerical model has been constructed, in which the fluid velocity field is calculated with an implicit lattice-Boltzmann method, and the transport of dissolved species is modeled by an innovative random walk algorithm that incorporates the chemical kinetics at the solid surfaces. The model contains no free parameters or semi-empirical mass-transfer coefficients. The simulated morphological changes in a complex fracture are compared with recent laboratory experiments <Detwiler et al., 2003> with the same initial topography.