We construct supersymmetric M3-brane solutions in D = 11 supergravity. They can be viewed as deformations of backgrounds taking the form of a direct product of four-dimensional Minkowski spacetime, and a non-compact Ricci-flat manifold of G(2) holonomy. Although the 4-form field strength is turned on it carries no charge, and the 3-branes are correspondingly massless. We also obtain 3-branes of a different type, arising as M5-branes wrapped over S-2. (C) 2001 Published by Elsevier Science B.V.