We observe a sixfold Purcell broadening of the D2 line of an optically trapped 87 Rb atom strongly coupled to a fiber cavity. Under external illumination by a near-resonant laser, up to 90% of the atom's fluorescence is emitted into the resonant cavity mode. The sub-Poissonian statistics of the cavity output and the Purcell enhancement of the atomic decay rate are confirmed by the observation of a strongly narrowed antibunching dip in the photon autocorrelation function. The photon leakage through the higher-transmission mirror of the single-sided resonator is the dominant contribution to the field decay (κ ≈ 2π×50 MHz), thus offering a high-bandwidth, fiber-coupled channel for photonic interfaces such as quantum memories and single-photon sources.