We investigate the use of the Cell Broadband Engine (Cell/BE) for Combinatorial Optimization applications. We present a parallel version of a constraint-based Local Search algorithm which was chosen because it fits very well the Cell/BE architecture since it requires neither shared memory nor communication between processors. The performance study on several large optimization benchmarks shows mostly linear time speedups, even sometimes super-linear. These experiments were done on a Dual-Cell IBM Blade with 16 processors. Besides getting speedups, the execution times exhibit a much smaller variance, which benefits applications where a timely reply is critical.