Errors in sample handling or test interpretation may cause false positives in forensic DNA testing. This article uses a Bayesian model to show how the potential for a false positive affects the evidentiary value of DNA evidence and the sufficiency of DNA evidence to meet traditional legal standards for conviction. The Bayesian analysis is contrasted with the “false positive fallacy,” an intuitively appealing but erroneous alternative interpretation. The findings show the importance of having accurate information about both the random match probability and the false positive probability when evaluating DNA evidence. It is argued that ignoring or underestimating the potential for a false positive can lead to serious errors of interpretation, particularly when the suspect is identified through a “DNA dragnet” or database search, and that ignorance of the true rate of error creates an important element of uncertainty about the value of DNA evidence.