We have used Hubble/WFC3 and the G141 grism to measure the secondary eclipse of the transiting, very hot Jupiter CoRoT-2b in the 1.1-1.7 μm spectral region. We find an eclipse depth averaged over this band equal to parts per million, equivalent to a blackbody temperature of 1788 ± 18 K. We study and characterize several WFC3 instrumental effects, especially the "hook" phenomenon described by Deming et al. We use data from several transiting exoplanet systems to find a quantitative relation between the amplitude of the hook and the exposure level of a given pixel. Although the uncertainties in this relation are too large to allow us to develop an empirical correction for our data, our study provides a useful guide for optimizing exposure levels in future WFC3 observations. We derive the planet's spectrum using a differential method. The planet-to-star contrast increases to longer wavelength within the WFC3 bandpass, but without water absorption or emission to a 3σ limit of 85 ppm. The slope of the WFC3 spectrum is significantly less than the slope of the best-fit blackbody. We compare all existing eclipse data for this planet to a blackbody spectrum, and to spectra from both solar abundance and carbon-rich (C/O = 1) models. A blackbody spectrum is an acceptable fit to the full data set. Extra continuous opacity due to clouds or haze, and flattened temperature profiles, are strong candidates to produce quasi-blackbody spectra, and to account for the amplitude of the optical eclipses. Our results show ambiguous evidence for a temperature inversion in this planet.