We present Spitzer Space Telescope infrared photometric time series of the transiting extrasolar planet system TrES-1. The data span a predicted time of secondary eclipse, corresponding to the passage of the planet behind the star. In both bands of our observations, we detect a flux decrement with a timing, amplitude, and duration as predicted by published parameters of the system. This signal represents the first direct detection of (i.e., the observation of photons emitted by) a planet orbiting another star. The observed eclipse depths (in units of relative flux) are 0.00066+/-0.00013 at 4.5 μm and 0.00225+/-0.00036 at 8.0 μm. These estimates provide the first observational constraints on models of the thermal emission of hot Jupiters. Assuming that the planet emits as a blackbody, we estimate an effective temperature of Tp=1060+/-50 K. Under the additional assumptions that the planet is in thermal equilibrium with the radiation from the star and emits isotropically, we find a Bond albedo of A=0.31+/-0.14. This would imply that the planet absorbs the majority of stellar radiation incident upon it, a conclusion of significant impact to atmospheric models of these objects. We also compare our data to a previously published model of the planetary thermal emission, which predicts prominent spectral features in our observational bands due to water and carbon monoxide. This model adequately reproduces the observed planet-to-star flux ratio at 8.0 μm however, it significantly overpredicts the ratio at 4.5 μm. We also present an estimate of the timing of the secondary eclipse, which we use to place a strong constraint on the expression ecosω, where e is the orbital eccentricity and ω is the longitude of periastron. The resulting upper limit on e is sufficiently small that we conclude that tidal dissipation is unlikely to provide a significant source of energy interior to the planet.