In Coulomb drag, a current flowing in one conductor can induce a voltage across an adjacent conductor via the Coulomb interaction. The mechanisms yielding drag effects are not always understood, even though drag effects are sufficiently general to be seen in many low-dimensional systems. In this Letter, we observe Coulomb drag in a Coulomb-coupled double quantum dot (CC-DQD) and, through both experimental and theoretical arguments, identify cotunneling as essential to obtaining a correct qualitative understanding of the drag behavior.