  We demonstrate an all-fiber cavity QED system with a trapped single atom in
the strong coupling regime. We use a nanofiber Fabry-Perot cavity, that is, an
optical nanofiber sandwiched by two fiber-Bragg-grating mirrors. Measurements
of the cavity transmission spectrum with a single atom in a state-insensitive
nanofiber trap clearly reveal the vacuum Rabi splitting.
