The nuclear magnetic resonance of Al27 in UAl2 has been observed in the range of temperatures 4-300°K. Large Knight shifts (K) were found with a temperature dependence not of a Curie-Weiss type. This behavior and the temperature independence of the linewidth, when considered in conjunction with susceptibility (χ) measurements, indicate (1) no localization of the magnetization of the U (5f and/or 6d) electrons and (2) no magnetic ordering exists. These results are contrasted with those obtained on the isostructural XAl2 (X=rare-earth ion) metals. Using a simple model, certain features of the band structure and the effective exchange interaction between itinerant f and s electrons may be deduced. From the extrapolated limit of the linear K vs χ curve a large positive temperature-independent contribution to χ is obtained which is attributable to the Kubo-Obata orbital paramagnetism to be expected in metals with unfilled degenerate bands.