We report the use of coherent anti-Stokes Raman spectroscopy (CARS) in gas-filled hollow-core photonic crystal fiber (HC-PCF) for trace gas detection. The long optical path-lengths yield a 60 dB increase in the signal level compared with free-space arrangements. This enables a relatively weak supercontinuum (SC) to be used as Stokes seed, along with a ns pump pulse, paving the way for broadband (>4000 cm-1) single-shot CARS with an unprecedented resolution of ∼100 MHz. A kagomé-style HC-PCF provides broadband guidance, and, by operating close to the pressure-tunable zero dispersion wavelength, we can ensure simultaneous phase-matching of all gas species. We demonstrate simultaneous measurement of the concentrations of multiple trace gases in a gas sample introduced into the core of the HC-PCF.