Two popular optimal search-based solvers for the multi-agent pathfinding (MAPF) problem, Conflict-Based Search (CBS) and Increasing Cost Tree Search (ICTS), have been extended separately for continuous time domains and symmetry breaking. However, an approach to symmetry breaking in continuous time domains remained elusive. In this work, we introduce a new algorithm, Conflict-Based Increasing Cost Search (CBICS), which is capable of symmetry breaking in continuous time domains by combining the strengths of CBS and ICTS. Our experiments show that CBICS often finds solutions faster than CBS and ICTS in both unit time and continuous time domains.