Provided is an apparatus for supplying lubricant to a timing chain installed in an engine, the apparatus including an injection hole configured for injecting lubricant from an oil pump, and an inner cover having a guide groove configured to receive lubricant injected from the injection hole and guide the lubricant toward a engagement place between the timing chain and a sprocket, wherein the inner cover has a guide groove provided at a position facing an injection hole of a counter surface portion that is spaced apart from a cylinder block and faces the guide groove.