We experimentally demonstrated synchronization of chaos in a master-slave type set-up with two diode-pumped Nd:YVO4 microchip lasers (λ=1064 nm) for the first time. Chaotic output in the microchip lasers is easily obtained by modulating the injection current of the laser diode for pumping (pump modulation) near the relaxation oscillation frequency (∼MHz). The relatively low relaxation oscillation frequencies compared with those of laser diodes (∼GHz) make it easy to observe and control the chaos in the microchip solid-state lasers. To realize more accurate synchronization, the injected power into the slave laser cavity should be increased. We observed that the variance of the correlation plot decreases with increasing injected power. Moreover stable synchronization can also be obtained under higher injected power since the injection locking range is proportional to the square root of the injected power.