The standard (AGM) approach to belief change assumes that the underlying logic is at least as strong as classical propositional logic. This paper investigates an account of belief change, specifically contraction, where the underlying logic is that governing Horn clauses. Thus this work sheds light on the theoretical underpinnings of belief change by weakening a fundamental assumption of the area. This topic is also of independent interest since Horn clauses have been used in areas such as deductive databases and logic programming. It proves to be the case that there are two distinct classes of contraction functions for Horn clauses: e-contraction, which applies to entailed formulas, and i-contraction, which applies to formulas leading to inconsistency. E-contraction is applicable in yet weaker systems where there may be no notion of negation (such as in definite clauses). I-contraction on the other hand has severe limitations, which makes it of limited use as a belief change operator. In both cases we explore the class of maxichoice functions which, we argue, is the appropriate approach for contraction in Horn clauses theories.