We report on a 12 hr XMM-Newton observation of the supergiant High-Mass X-ray Binary IGR J16207-5129. This is only the second soft X-ray (0.4-15 keV, in this case) study of the source since it was discovered by the INTEGRAL satellite. The average energy spectrum is very similar to those of neutron star HMXBs, being dominated by a highly absorbed power-law component with a photon index of 1.15. The spectrum also exhibits a soft excess below 2 keV and an iron Kalpha emission line at 6.39+/-0.03 keV. For the primary power-law component, the column density is 1.19E23 cm^-2, indicating local absorption, likely from the stellar wind, and placing IGR J16207-5129 in the category of obscured IGR HMXBs. The source exhibits a very high level of variability with an rms noise level of 64%+/-21% in the 0.0001 to 0.05 Hz frequency range. Although the energy spectrum suggests that the system may harbor a neutron star, no pulsations are detected with a 90% confidence upper limit of 2% in a frequency range from 0.0001 to 88 Hz. We discuss similarities between IGR J16207-5129 and other apparently non-pulsating HMXBs, including other IGR HMXBs as well as 4U 2206+54 (but see arXiv:0812.2365) and 4U 1700-377.
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