We present the first measurements of the near-infrared (NIR), specifically the J-band, sky background in the Canadian High Arctic. There has been considerable recent interest in the development of an astronomical observatory in Ellesmere Island; initial site testing has shown promise for a world-class site. Encouragement for our study came from sky background measurements on the high Antarctic glacial plateau in winter that showed markedly lower NIR emission when compared to good mid-latitude astronomical sites due to reduced emission from the Meinel bands, i.e. hydroxyl radical (OH) airglow lines. This is possibly a Polar effect and may also be present in the High Arctic. To test this hypothesis, we carried out an experiment which measured the the J-band sky brightness in the High Arctic during winter. We constructed a zenith-pointing, J-band photometer, and installed it at the Polar Environment Atmospheric Research Laboratory (PEARL) near Eureka, Nunavut (latitude: 80° N). We present the design of our ruggedized photometer and our results from our short PEARL observing campaign in February 2012. Taken over a period of four days, our measurements indicate that the J-band sky brightness varies between 15.5-15.9 mag arcsec2 with a measurement uncertainty of 0.15 mag. The uncertainty is entirely dominated by systematic errors present in our radiometric calibration. On our best night, we measured a fairly consistent sky brightness of 15.8 +/- 0.15 mag arcsec2. This is not corrected for atmospheric extinction, which is typically < 0.1 mag in the J-band on a good night. The measured sky brightness is comparable to an excellent mid-latitude site, but is not as dark as claimed by the Antarctic measurements. We discuss possible explanations of why we do not see as dark skies as in the Antarctic. Future winter-long sky brightness measurements are anticipated to obtain the necessary statistics to make a proper comparison with the Antarctic measurements.