A 3.1-3.7-micron spectrum of the classical Be star Beta Mon A is presented at a resolution of lambda/Delta-lambda of 700-800. The spectrum shows strong hydrogen recombination lines, including Pf-delta and a series of Humphreys lines from Hu 19 to Hu 28. The relative recombination line strengths suggest that Pf-delta has a large optical depth. The Humphreys lines have relative strengths consistent with case B and may be optically thin. The line widths observed are broader than the Balmer lines and similar in width to Fe II lines, consistent with a disk model in which optically thinner lines arise primarily from a faster rotating inner disk, while optically thicker lines come mainly from a slower rotating outer disk. The apparent lack of Stark broadening of the Humphreys lines is used to place an upper limit on the circumstellar electron density of about 10 exp 12/cu cm.