The Wilson cloud chamber, invented in 1911 by Scottish physicist Charles Wilson, is a remarkably simple and effective charged particle detector. Cloud chambers were used regularly in particle physics experiments for decades, until being supplanted by bubble chambers. In this article, we describe a lab activity that is suitable for introductory-level physics students using a cloud chamber to measure the rate of alpha decay in the atmosphere. In performing this experiment, the students deepen their understanding of alpha decay, including the random nature of the process. They also become acquainted with statistical uncertainties from measuring a random process.