We report the results of long-slit, CCD observations of the optical continuum of the planetary nebula NGC 7027 where we observe the broad luminescence band known as extended red emission (ERE) which has previously only been detected in reflection nebulae and the peculiar object HD 44179. We map the spatial distribution of ERE across the nebula in an east-west direction and find that it is emitted predominantly from a shell situated outside the ionized volume of the nebula. We find the ERE to be cospatial with and possibly more extensive than the distribution of the 3.28 μm "unidentified" infrared emission feature attributed to various hydrocarbons. We discuss the energetics of this emission process and show that there is sufficient energy in the UV-visible portion of the spectrum of the nebula to excite this luminescence.