We report on the highly efficient, octave-spanning mid-infrared (mid-IR) optical parametric amplification (OPA) in a ZnGeP2 (ZGP) crystal, pumped by a 1 kHz, 2.4 μm, 250 fs Cr:ZnSe chirped-pulse amplifier. The full spectral coverage of 3-10 μm with the amplified signal and idler beams is demonstrated. The signal beam in the range of ~3 -5 μm is produced by either white light generation (WLG) in YAG or optical parametric generation (OPG) in ZGP using the common 2.4 μm pump laser. We demonstrate the pump to signal and idler combined conversion efficiency of 23% and the pulse energy of up to 130 μJ with ~2 μJ OPG seeding, while we obtain the efficiency of 10% and the pulse energy of 55 μJ with ~0.2 μJ WLG seeding. The OPA output energy is limited by the available pump pulse energy (0.55 mJ at ZGP crystal) and therefore further energy scaling is feasible with multi-stage OPA and higher pump pulse energy. The autocorrelation measurements based on random quasi-phase matching show that the signal pulse durations are ~318 fs and ~330 fs with WLG and OPG seeding, respectively. In addition, we show the spectrally filtered 30 μJ OPA output at 4.15 μm suitable for seeding a Fe:ZnSe amplifier. Our ultrabroadband femtosecond mid-IR source is attractive for various applications, such as strong-field interactions, dielectric laser electron acceleration, molecular spectroscopy, and medical surgery.