A height adjustable chair armrest includes an armrest top portion and a supporting member coupled with a chair body. The supporting member includes an outer tube and an inner tube received in the outer tube. The inner tube includes a plurality of positioning holes. A resilient member is mounted in the inner tube and includes a body and a resilient plate slantingly branching from the body. A first peg is disposed on the body and is releasably engaged in one of the plurality of positioning holes. An actuation rod is insertable through the outer tube into an operational hole of the body to press against or release the resilient plate. A rib is disposed on an inner periphery of the inner tube and is spaced from a top end of the inner tube by a spacing. The resilient member is restrained at a side of the rib.