We introduce the study of Conditional symmetry breaking in constraint programming. This arises in a sub-problem of a constraint satisfaction problem, where the sub-problem satisfies some condition under which additional symetries hold. Conditional symmetry can cause redundancy in a systematic search for solutions. Breaking this symmetry is an important part of solving a constraint satisfaction problem effectively. We demonstrate experimentally that three methods, well-known for breaking unconditional symmetries, can be applied to conditional symmetries. These are: adding conditional symmetry-breaking constraints, reformulating the problem to remove the symmetry, and augmenting the search process to break the conditional symmetry dynamically through the use of a variant of Symmetry Breaking by Dominance Detection (SBDD). We thank Alan Frisch and Chris Jefferson. Ian Gent is supported by a Royal Society of Edinburgh SEELLD/RSE Support Research Fellowship. Ian Miguel is supported by a UK Royal Academy of Engineering/EPSRC Research Fellowship. This material is based in part on works supported by the Science Foundation Ireland under Grant No. 00/PI.1/C075.