The invention provides a low-profile, dome-shaped body for attachment to a scleral surface of an eye and defining an internal cavity for receiving a drug or other pharmaceutically active agent. The device has an opening for controllably delivering the drug into the eye at therapeutically effective concentrations over a prolonged period of time. When attached, the device does not affect or otherwise restrict movement of the eye. Features of the invention include an optional drug inlet port and puncture guard, both designed for refilling the device while preventing a needle inserted through the inlet port from contacting the sclera.