The First Detections of the Extragalactic Background Light at 3000, 5500, and 8000 Å. I. Results

(Abridged) We present the first detections of the mean flux of the optical extragalactic background light (EBL) at 3000, 5500, and 8000A. Diffuse foreground flux at these wavelengths comes from terrestrial airglow, dust-scattered sunlight (zodiacal light), and dust-scattered Galactic starlight (diffuse Galactic light). We have avoided the brightest of these, terrestrial airglow, by measuring the absolute surface brightness of the night sky from above the Earth's atmosphere using the Wide Field Planetary Camera2 (WFPC2) and Faint Object Spectrograph (FOS), both aboard the Hubble Space Telescope (HST). On the ground, we have used the duPont 2.5 m Telescope at Las Campanas Observatory (LCO) to obtain contemporaneous spectrophotometry of ``blank'' sky in the HST field of view to measure and then subtract foreground zodiacal light from the HST observations. We have minimized the diffuse Galactic light in advance by selecting the HST target field along a line of sight with low Galactic dust column density, and then estimated the low--level Galactic foreground using a simple scattering model and the observed correlation between thermal, 100 micron emission and optical scattered flux from the same dust. In this paper, we describe the coordinated LCO/HST program and the HST observations and data reduction, and present the resulting measurements of the EBL.