A safety lock system for cabinet drawers that provides a lock mechanism that in a locked position prevents any drawer from opening and in an unlocked position allows only one drawer to be opened at any one time. The system includes a slide wedge-ended member attached to each drawer, an inner cabinet wall and a support member both of which include vertically aligned T-shaped slots for receiving interlock pieces. Each interlock piece includes an upper protrusion and a lower protrusion and a spacer bar connecting the two protrusions.