We report the creation of a Bose-Einstein condensate using buffer-gas cooling, the first realization of BEC using a method which relies neither on laser cooling nor unique atom-surface properties. Metastable helium ( ⁴He*) is buffer-gas cooled and magnetically trapped using an optimized buffer-gas trapping apparatus, followed by evaporative cooling to quantum degeneracy. Evaporative cooling proceeds in two stages, each traversing approximately five orders of magnitude in phase space density. An initial stage of evaporation uses a surface to adsorb atoms, while a later stage uses radio-frequency induced spin-flips to evaporate atoms. Trapped atoms are detected using absorption and phase-contrast imaging both in-situ and in time-of-flight expansion. 10¹¹ atoms are initially trapped, leading to Bose-Einstein condensation at a critical temperature of 5 μK and threshold atom number of 1.1 x 10⁶. The method developed here is applicable to a wide array of paramagnetic atoms as well as molecules, many of which are impractical to laser cool and all of which are impossible to surface cool.