Holography is a new and exciting field that has found many applications in physics and engineering. Atomic spectroscopy has been the experimental cornerstone of modern physics and chemistry. This paper reports on an intermediate undergraduate laboratory experiment that combines fundamental ideas and techniques of both fields. The student utilizes holographic techniques to make a small sinusoidal diffraction grating and then uses this grating to analyze the spectrum of hydrogen. The Rydberg constant can be determined from the wavelength, the angle between the laser beams used to make the grating, and the observed diffractions angles of lines of the Balmer series.