We present deep optical 18-medium-band photometry from the Subaru telescope over the {approx}30' x 30' Extended Chandra Deep Field-South, as part of the Multiwavelength Survey by Yale-Chile (MUSYC). This field has a wealth of ground- and space-based ancillary data, and contains the GOODS-South field and the Hubble Ultra Deep Field. We combine the Subaru imaging with existing UBVRIzJHK and Spitzer IRAC images to create a uniform catalog. Detecting sources in the MUSYC 'BVR' image we find {approx}40,000 galaxies with R {sub AB} < 25.3, the median 5{sigma} limit of the 18 medium bands. Photometric redshifts are determined using the EAzY code and compared to {approx}2000 spectroscopic redshifts in this field. The medium-band filters provide very accurate redshifts for the (bright) subset of galaxies with spectroscopic redshifts, particularly at 0.1 < z < 1.2 and at z {approx}> 3.5. For 0.1 < z < 1.2, we find a 1{sigma} scatter in {Delta}z/(1 + z) of 0.007, similar to results obtained with a similar filter set in the COSMOS field. As a demonstration of the data quality, we show that the red sequence and blue cloud can be cleanly identified in rest-frame color-magnitude diagrams at 0.1 < z < 1.2. We find that {approx}20% of the red sequence galaxies show evidence of dust emission at longer rest-frame wavelengths. The reduced images, photometric catalog, and photometric redshifts are provided through the public MUSYC Web site.