Transcriptional positive-feedback loops are widely associated with bistability, characterized by two stable expression states that allow cells to respond to analog signals in a digital manner. Using a synthetic system in budding yeast, we show that positive feedback involving a promoter with multiple transcription factor (TF) binding sites can induce a steady-state bimodal response without cooperative binding of the TF. Deterministic models of this system do not predict bistability. Rather, the bimodal response requires a short-lived TF and stochastic fluctuations in the TF's expression. Multiple binding sites provide these fluctuations. Because many promoters possess multiple binding sites and many TFs are unstable, positive-feedback loops in gene regulatory networks may exhibit bimodal responses, but not necessarily because of deterministic bistability, as is commonly thought.