We report the detection of the eclipse of the very-hot Jupiter WASP-12b via z-band time-series photometry obtained with the 3.5-meter ARC telescope at Apache Point Observatory. We measure a decrease in flux of 0.082+/-0.015% during the passage of the planet behind the star. That planetary flux is equally well reproduced by atmospheric models with and without extra absorbers, and blackbody models with f > 0.585+/-0.080. It is therefore necessary to measure the planet at other wavelengths to further constrain its atmospheric properties. The eclipse appears centered at phase = 0.5100 (+0.0072,-0.0061), consistent with an orbital eccentricity of |e cos w| = 0.016 (+0.011,-0.009) (see note at end of Section 4). If the orbit of the planet is indeed eccentric, the large radius of WASP-12b can be explained by tidal heating.
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