An oil pump mechanism is incorporated in a chain saw having a centrifugal clutch and a saw chain adapted to be driven through the centrifugal clutch and activated in synchronization with the centrifugal clutch to supply a lubricating oil to the saw chain. The mechanism includes a crankshaft, a clutch shoe being mounted on the centrifugal clutch and being connected in driven relation to the crankshaft, a clutch drum disposed coaxially around the crankshaft, a worm fitted on the crankshaft by insertion in a freely rotatable manner and connected in driven relation to the clutch drum to be integrally rotated with the clutch drum, a driven gear engaged with the worm, and a movable pumping element for pumping the lubricating oil. The worm has an inner portion located opposed to the crankshaft and an outer portion including a tooth region. The inner portion is made of self-lubricating resin and the outer portion is made of wear-resistant metal.