Models of the offense chain have held that sexual offenses occur as a culmination of a chain of actions on the part of the perpetrator. While this idea has been used to develop cognitive behavioral models of relapse prevention, quantitative tests of the offense chain hypothesis have been rare. The current study developed a simple and statistically testable mathematical model of the offense chain and tested it on a sample of seven intellectually disabled adult sexual offenders. The model incorporates a threshold corresponding to either a lapse or a relapse, depending on the severity of the behavior. It was hypothesized that the threshold model would better capture the time series of offender behaviors than a linear model. Data included archival daily records of the negative behaviors of the seven participants who lived in a residential program between 1995 and 2000. Results of time series analyses suggested support for the idea of an offense chain of sexual offending. Increases in negative behaviors were likely to follow attempts at control. Future research should attempt to replicate these findings with other types of offender groups. Figures, tables, notes, references