The observability of space object attitude from light curve data is analyzed. Light curves, which are the time-varying apparent brightness of sunlight reflected off a space object and measured by an observer, depend on the object position, attitude, surface material, shape, and other parameters. Previous work employing light curve data for shape estimation requires the availability of good attitude estimates. This paper explores the possibility of obtaining attitude information from the brightness measurements themselves. Some types of attitude estimate errors are detectable from individual brightness measurements, but other attitude errors lie in the nullspace of the Fisher information matrix and are not observable in the static case. Analytical expressions for the nullspace vectors are derived. The observability of the light curve model parameters is also briefly addressed.