An experimental platform operating at the level of individual quanta and providing strong light-matter coupling is a key requirement for quantum information processing. In our work, we show that hollow-core photonic bandgap fibers filled with laser-cooled atoms might serve as such a platform, despite their typical complicated birefringence properties. To this end, we present a detailed theoretical and experimental study to identify a fiber with suitable properties to achieve operation at the single-photon level. In the fiber, we demonstrate the storage and on-demand retrieval as well as the creation of stationary light pulses, based on electromagnetically induced transparency, for weak coherent light pulses down to the single-photon level with an unconditional noise floor of 0.017(4) photons per pulse. These results clearly demonstrate the prospects of such a fiber-based platform for applications in quantum information networks.