Commercial picosecond sources have found widespread applications. Typical system parameters are pulse widths below 20 ps, repetition rates between 0.1 and 2 MHz, and microjoule level pulse energies. Most systems are based on short pulse mode-locked oscillators, regenerative amplifiers, and pockel cells as active beam switches. In contrast, we present a completely passive system, consisting of a passively Q-switched microchip laser, a single-stage amplifier, and a pulse compressor. The Q-switched microchip laser has a 50-μm-long Nd:YVO4 gain material optically bonded to a 4.6-mm-thick undoped YVO4 crystal. It delivers pulse widths of 40 ps and repetition rates of 0.2 to 1.4 MHz at a wavelength of 1.064 μm. The pulse energy is a few nanojoule. These 40-ps pulses are spectrally broadened in a standard single-mode fiber and then compressed in a 24-mm-long chirped Bragg grating to as low as 3.3 ps. The repetition rate can be tuned from ∼0.2 to 1.4 MHz by changing the pump power, while the pulse width and the pulse energy from the microchip laser are unchanged. The spectral broadening in the fiber is observed throughout the pulse repetition rate, supporting sub-10-ps pulses. Finally, the pulses are amplified in a single-stage Nd:YVO4 amplifier up to the microjoule level (up to 4 μJ pulse energy). As a result, the system delivers sub-10-ps pulses at a microjoule level with about 1 MHz repetition rate, and thus fulfills the requirements for ps-micromachining. It does not contain any active switching elements and can be integrated in a very compact setup.