Abstract Satisfiability Modulo Constraint Handling Rules (SMCHR) is the integration of the Constraint Handling Rules (CHRs) solver programming language into a Satisfiability Modulo Theories (SMT) solver framework. Constraint solvers are implemented in CHR as a set of high-level rules that specify the simplification (rewriting) and constraint propagation behavior. The traditional CHR execution algorithm manipulates a global store representing a flat conjunction of constraints. This paper introduces SMCHR: a tight integration of CHR with a modern Boolean Satisfiability (SAT) solver. Unlike CHR, SMCHR can handle (quantifier-free) formulae with an arbitrary propositional structure. SMCHR is essentially a Satisfiability Modulo Theories (SMT) solver where the theory T is implemented in CHR.