Observations from the first flight of the Medium Scale Anisotropy Measurement (MSAM) are analyzed to place limits on Gaussian fluctuations in the Cosmic Microwave Background Radiation (CMBR). This instrument chops a 30arcmin beam in a 3 position pattern with a throw of $pm40arcmin$; the resulting data is analyzed in statistically independent single and double difference datasets. We observe in four spectral channels at 5.6, 9.0, 16.5, and 22.5~icm, allowing the separation of interstellar dust emission from CMBR fluctuations. The dust component is correlated with the IRAS 100~micron map. The CMBR component has two regions where the signature of an unresolved source is seen. Rejecting these two source regions, we obtain a detection of fluctuations which match CMBR in our spectral bands of $0.6 times 10^{-5} < Delta T/T < 2.2 times 10^{-5}$ (90% CL interval) for total rms Gaussian fluctuations with correlation angle 0fdg5, using the single difference demodulation. For the double difference demodulation, the result is $1.1 times 10^{-5} < Delta T/T < 3.1 times 10^{-5}$ (90% CL interval) at a correlation angle of 0fdg3.