Telecom C-band single photons exhibit the lowest attenuation in optical fibers, enabling long-haul, quantum-secured communication. However, efficient coupling with optical fibers is crucial for these single photons to be effective carriers in long-distance transmission. We demonstrate an efficient fiber-coupled single photon source in the telecom C-band using InAs/InP quantum dots coupled to a tapered nanobeam. The tapered nanobeam structure facilitates directional emission that is mode-matched to a lensed fiber, resulting in a collection efficiency of up to 65% from the nanobeam to the single-mode fiber. Using this approach, we demonstrate single photon count rates of 575 +/- 5 Kcps and a single photon purity of g((2)) (0) = 0.015 +/- 0.003. Additionally, we demonstrate Hong-Ou-Mandel interference from the emitted photons with a visibility of 0.84 +/- 0.06. From these measurements, we determine a photon coherence time of 450 +/- 20 ps, a factor of only 8.3 away from the lifetime limit. This work represents an important step toward the development of telecom C-band single-photon sources emitting bright, pure, and indistinguishable photons, which are necessary to realize fiber-based long-distance quantum networks.