We derive galaxy source counts at 70 and 160 microns using the Multiband Imaging Photometer for Spitzer (MIPS) to map the Chandra Deep Field South (CDFS) and other fields. At 70 microns, our observations extend upwards about 2 orders of magnitude in flux density from a threshold of 15 mJy, and at 160 microns they extend about an order of magnitude upward from 50 mJy. The counts are consistent with previous observations on the bright end. Significant evolution is detected at the faint end of the counts in both bands, by factors of 2-3 over no-evolution models. This evolution agrees well with models that indicate most ofthe faint galaxies lie at redshifts between 0.7 and 0.9. The new Spitzer data already resolve about 23% of the Cosmic Far Infrared Background at 70 microns and about 7% at 160 microns.