Infrared Dark Clouds (IRDCs) are cold, high mass surface density and high density structures, likely to be representative of the initial conditions for massive star and star cluster formation. CO emission from IRDCs has the potential to be useful for tracing their dynamics, but may be affected by depleted gas phase abundances due to freeze-out onto dust grains. Here we analyze C18O J=1-0 and J=2-1 emission line data, taken with the IRAM 30m telescope, of the highly filamentary IRDC G035.39.-0033. We derive the excitation temperature as a function of position and velocity, with typical values of ~7K, and thus derive total mass surface densities, Sigma_C18O, assuming standard gas phase abundances and accounting for optical depth in the line, which can reach values of ~1. The mass surface densities reach values of ~0.07 g/cm^2. We compare these results to the mass surface densities derived from mid-infrared (MIR) extinction mapping, Sigma_SMF, by Butler & Tan, which are expected to be insensitive to the dust temperatures in the cloud. With a significance of >10sigma, we find Sigma_C18O/Sigma_SMF decreases by about a factor of 5 as Sigma increases from ~0.02 to ~0.2 g/cm^2, which we interpret as evidence for CO depletion. Several hundred solar masses are being affected, making this one of the most massive clouds in which CO depletion has been observed directly. We present a map of the depletion factor in the filament and discuss implications for the formation of the IRDC.
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