The Galactic HII region luminosity function (LF) is an important metric for understanding global star formation properties of the Milky Way, but only a few studies have been done and all use relatively small numbers of HII regions. We use a sample of 797 first Galactic quadrant HII regions compiled from the WISE Catalog of Galactic HII Regions to examine the form of the LF at multiple infrared and radio wavelengths. Our sample is statistically complete for all regions powered by single stars of type O9.5V and earlier. We fit the LF at each wavelength with single and double power laws. Averaging the results from all wavelengths, the mean of the best-fit single power law index is $langlealpharangle=-1.75,pm,0.01$. The mean best-fit double power law indices are $langlealpha_1rangle=-1.40,pm,0.03$ and $langlealpha_2rangle=-2.33,pm,0.04$. We conclude that neither a single nor a double power law is strongly favored over the other. The LFs show some variation when we separate the HII region sample into subsets by heliocentric distance, physical size, Galactocentric radius, and location relative to the spiral arms, but blending individual HII regions into larger complexes does not change the value of the power law indices of the best-fit LF models. The consistency of the power law indices across multiple wavelengths suggests that the LF is independent of wavelength. This implies that infrared and radio tracers can be employed in place of H$alpha$.
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