Unlike photons, which are conveniently handled by mirrors and optical fibres without loss of coherence, atoms lose their coherence via atom-atom and atom-wall interactions. This decoherence of atoms deteriorates the performance of atomic clocks and magnetometers, and also hinders their miniaturization. Here we report a novel platform for precision spectroscopy. Ultracold strontium atoms inside a kagome-lattice hollow-core photonic crystal fibre are transversely confined by an optical lattice to prevent atoms from interacting with the fibre wall. By confining at most one atom in each lattice site, to avoid atom-atom interactions and Doppler effect, a 7.8-kHz-wide spectrum is observed for the S-1(0) - P-3(1) (m 0) transition. Atoms singly trapped in a magic lattice in hollow-core photonic crystal fibres improve the optical depth while preserving atomic coherence time.