We present Spitzer Space Telescope time series photometry of the exoplanet system HD 189733 spanning two times of secondary eclipse, when the planet passes out of view behind the parent star. We estimate the relative eclipse depth in five distinct bands and find the planet-to-star flux ratio to be 0.256% ± 0.014% (3.6 μm), 0.214% ± 0.020% (4.5 μm), 0.310% ± 0.034% (5.8 μm), 0.391% ± 0.022% (8.0 μm), and 0.598% ± 0.038% (24 μm). For consistency, we reanalyze a previously published time series to deduce a contrast ratio in an additional band, 0.519% ± 0.020% (16 μm). Our data are strongly inconsistent with a Planck spectrum, and we clearly detect emission near 4 μm as predicted by published theoretical models in which this feature arises from a corresponding opacity window. Unlike recent results for the exoplanet HD 209458b, we find that the emergent spectrum from HD 189733b is best matched by models that do not include an atmospheric temperature inversion. Taken together, these two studies provide initial observational support for the idea that hot Jupiter atmospheres diverge into two classes, in which a thermal inversion layer is present for the more strongly irradiated objects.