We describe the GENI Experiment Engine, a Distributed-Platform-as-a-Service facility designed to be implemented on a distributed testbed or infrastructure. The GEE is intended to provide rapid and convenient access to a distributed infrastructure for simple, easy-to-configure experiments and applications. Specifically, the design goal of the GEE is to permit experimenters and application writers to: (a) allocate a GEE slicelet; (b) deploy a simple experiment or application; (c) run the experiment; (d) collect the results; and (e) tear down the experiment, starting from scratch, within five minutes. The GEE consists of a set of cooperating services over the GENI infrastructure, which together with rapidly-allocated slicelets and a rapidly-allocated network offers a complete, ready to use, sliceable platform over the GENI Infrastructure. The GEE is designed to use off-the-shelf components and infrastructure; unlike previous PaaS offerings, it can be nested nicely inside a GENI slice, or any other IaaS infrastructure. Further, the GEE's southbound interface is extremely small and lightweight, making it portable to other underlying infrastructures.