A plastic scintillator paddle detector with embedded fiber light guides and photomultiplier tube readout, referred to as the Reaction Plane Detector (RXNP), was designed and installed in the PHENIX experiment prior to the 2007 run of the Relativistic Heavy Ion Collider (RHIC). The RXNP's design is optimized to accurately measure the reaction plane (RP) angle of heavy-ion collisions, where, for mid-central sNN=200GeV Au+Au collisions, it achieved a 2nd harmonic RP resolution of ∼0.75, which is a factor of ∼2 greater than PHENIX's previous capabilities. This improvement was accomplished by locating the RXNP in the central region of the PHENIX experiment, where, due to its large coverage in pseudorapidity (1.0<|η|<2.8) and ϕ(2π), it is exposed to the high particle multiplicities needed for an accurate RP measurement. To enhance the observed signal, a 2-cm Pb converter is located between the nominal collision region and the scintillator paddles, allowing neutral particles produced in the heavy-ion collisions to contribute to the signal through conversion electrons. This paper discusses the design, operation and performance of the RXNP during the 2007 RHIC run.