The novel coronavirus SARS-CoV-2 that causes the disease COVID-19 has forced us to go into our homes and limit our physical interactions with others. Economies around the world have come to a halt, with non-essential businesses being forced to close in order to prevent further propagation of the virus. Developing countries are having more difficulties due to their lack of access to diagnostic resources. In this study, we present an approach for detecting COVID-19 infections exclusively on the basis of self-reported symptoms. Such an approach is of great interest because it is relatively inexpensive and easy to deploy at either an individual or population scale. Our best model delivers a sensitivity score of 0.752, a specificity score of 0.609, and an area under the curve for the receiver operating characteristic of 0.728. These are promising results that justify continuing research efforts towards a machine learning test for detecting COVID-19.