We report the generation of tunable high-repetition-rate picosecond radiation in the mid-infrared using the new quasi-phase-matched nonlinear material of orientation-patterned gallium phosphide (OP-GaP). The source is realized by single-pass difference-frequency-generation (DFG) between the output signal of a picosecond optical parametric oscillator (OPO) tunable across 1609-1637 nm with input pump pulses at 1064 nm in OP-GaP, resulting in tunable radiation across 3040-3132 nm. Using a 40-mm-long crystal, we have generated up to 57 mW of DFG average power at ~80 MHz repetition rate for a pump power of 5 W and signal power of 0.9 W, with >30 mW over >50% of the tuning range. The DFG source exhibits a passive power stability better than 3.2% rms over 1 hour in good spatial beam quality. To the best of our knowledge, this is the first picosecond frequency conversion source based on OP-GaP.