We describe an achromatic, phase-stable, broadband source of polarization-entangled photon pairs with high spectral brightness that uses four-wave mixing in a fiber Sagnac interferometer. We achieved a polarization-entangled two-photon coincidence rate of 7 kHz per 0.5 THz (0.9 nm) of bandwidth per 300 mu W of average pump power. At this rate, we observed two-photon fringe interference visibilities greater than 97%, over a 10 THz (approximate to 21 nm) spectral range. We measured violations of Bell s inequality by more than 22 standard deviations for each of the four Bell states in less than 3 minutes per state. The high spectral brightness (26 kHz nm(-1) mW(-1)), large tunable wavelength range, single spatial mode, and phase stability make this source a promising candidate for a wide range of quantum-information applications.