We present results of the implementation of one MILC lattice QCD application-simulation with dynamical clover fermions using the hybrid-molecular dynamics R algorithm-on the Cell Broadband Engine processor. Fifty-four individual computational kernels responsible for 98.8% of the overall execution time were ported to the Cells Synergistic Processing Elements (SPEs). The remaining application framework, including MPI-based distributed code execution, was left to the Cells PowerPC processor. We observe that we only infrequently achieve more than 10 GFLOPS with any of the kernels, which is just over 4% of the Cells peak performance. At the same time, many of the kernels are sustaining a bandwidth close to 20 GB/s, which is 78% of the Cells peak. This indicates that the application performance is limited by the bandwidth between the main memory and the SPEs. In spite of this limitation, speedups of 8.7x (for 8x8x16x16 lattice) and 9.6x (for 16x16x16x16 lattice) were achieved when comparing a 3.2 GHz Cell processor to a single core of a 2.33 GHz Intel Xeon processor. When comparing the code scaled up to execute on a dual-Cell blade and a quad-core dual-chip Intel Xeon blade, the speedups are 1.5x (8x8x16x16 lattice) and 4.1x (16x16x16x16 lattice).