We report the processing of dense, superconducting MgB2 (rho approximate to 2.4 g cm(-3)) by an infiltration and growth technique. The process, which involves infiltration of liquid magnesium at 750 degrees C into a pre-defined boron precursor pellet, is relatively simple, results in the formation of a hard, dense structure and has the potential to fabricate large bulk samples of complex geometries. X-ray diffraction has been used to confirm the presence of the MgB2 primary phase with only residual magnesium content in the fully processed samples. The samples exhibit sharp superconducting transitions at 38.4 K and have critical current densities of up to 260 kA cm(-2) in self-field at 5 K. Modest measured values of H-c2(0) of 17 T suggest that superconductivity in bulk MgB2 fabricated by this technique is in the clean pairing limit.