When perceptually ambiguous stimuli are presented intermittently, the percept on one presentation tends to be the same as that on the previous presentation. The role of short-term, acute biases in the production of this perceptual stability is relatively well understood. In addition, however, long-lasting, chronic bias may also contribute to stability. In this paper we develop indices for both biases and for stability, and show that stability can be expressed as a sum of contributions from the two types of bias. We then apply this analytical procedure to binocular rivalry, showing that adjustment of the monocular contrasts can alter the relative contributions of the two biases. Stability is mainly determined by chronic bias when the contrasts are equal, but acute bias dominates stability when right-eye contrast is set lower than left-eye contrast. Finally, we show that the right-eye bias persists in continuous binocular rivalry. Our findings reveal a previously unappreciated contribution of chronic bias to stable perception.