For every operator space X the C * -algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finitedimensional representations). In particular, the free C * -algebra on any normed space so is. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.1991 Mathematics Subject Classification. 46L05, 46B28, 46M15.