Whispering-gallery mode (WGM) resonators combine small optical mode volumes with narrow resonance linewidths, making them exciting platforms for a variety of applications. Here we report a flying WGM microlaser, realized by optically trapping a dye-doped microparticle within a liquid-filled hollow-core photonic crystal fiber (HC-PCF) using a CW laser and then pumping it with a pulsed excitation laser whose wavelength matches the absorption band of the dye. The laser emits into core-guided modes that can be detected at the endfaces of the HC-PCF. Using radiation forces, the microlaser can be freely propelled along the HC-PCF over multi-centimeter distances-orders of magnitude farther than in previous experiments where tweezers and fiber traps were used. The system can be used to measure temperature with high spatial resolution, by exploiting the temperature-dependent frequency shift of the lasing modes, and may also permit precise delivery of light to remote locations.