We present a fiber-based source of polarization-entangled photons that is well suited for quantum communication applications in the 1550 nm band of standard fiber-optic telecommunications. Polarization entanglement is created by pumping a nonlinear-fiber Sagnac interferometer with two time-delayed orthogonally polarized pump pulses and subsequently removing the time distinguishability by passing the parametrically scattered signal and idler photon pairs through a piece of birefringent fiber. Coincidence detection of the signal and idler photons yields biphoton interference with visibility greater than 90%, while no interference is observed in direct detection of either signal or idler photons. All four Bell states can be prepared with our setup and we demonstrate violations of the Clauser-Horne-Shimony-Holt form of Bell's inequality by up to 10 standard deviations of measurement uncertainty.