We have observed a Bose-Einstein condensate in a dilute gas of 4He in the (3)2S(1) metastable state. We find a critical temperature of (4.7+/-0.5) microK and a typical number of atoms at the threshold of 8 x 10(6). The maximum number of atoms in our condensate is about 5 x 10(5). An approximate value for the scattering length a = (16+/-8) nm is measured. The mean elastic collision rate at threshold is then estimated to be about 2 x 10(4) s(-1), indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is 2 s, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.