We show, for the first time to our knowledge, all-fiber chirped pulse amplification using an air-core photonic bandgap fiber. Pulses from a wavelength- and duration-tunable femtosecond/picosecond source at 10 GHz were dispersed in 100 m of dispersion compensating fiber before being amplified in an erbium-doped fiber amplifier and subsequently recompressed in 10 m of the anomalously dispersive photonic bandgap fiber. Pulses as short as 1.1 ps were obtained. As air-core fibers present negligible nonlinearity, the presented configuration can potentially be used to obtain ultra-high pulse peak powers. A study of the air-core fiber dispersion and dispersion slope is also presented.