We present an alternate method of determining the progression of the solar cycle through an analysis of the solar X-ray background. Our results are based on the NOAA Geostationary Operational Environmental Satellites (GOES) X-ray data in the 1-8 Å band from 1986 to the present, covering solar cycles 22, 23, and 24. The X-ray background level tracks the progression of the solar cycle through its maximum and minimum. Using the X-ray data, we can therefore make estimates of the solar cycle progression and the date of solar maximum. Based upon our analysis, we conclude that the Sun reached its hemisphere-averaged maximum in solar cycle 24 in late 2013. This is within six months of the NOAA prediction of a maximum in spring 2013. © 2014. The American Astronomical Society. All rights reserved..