We demonstrate optical parametric chirped pulse amplification (OPCPA) at 1-kHz repetition rate in periodically poled stoichiometric LiTaO3 (PPSLT) with 1 mol % MgO doping. Diode pumping was used both for the fiber laser generating the femtosecond seed pulses and the nanosecond laser/amplifier employed as a pump source. The high gain ( approximately 63 dB) and large bandwidth (20 nm) obtained for single-stage nondegenerate OPCPA operation provide a compact and efficient solution for amplification of ultrashort pulses near 1.57 microm. Stretched femtosecond pulses could be amplified up to 39.5 microJ in a 7-mm long, 2-mm thick sample of PPSLT. The pulse duration of the amplified signal pulses (FWHM) after recompression amounted to 315 fs.