This paper concerns the development of a high-performance implementation of the Particle-in-Cell method for plasma simulation on Intel Xeon Phi coprocessors. We discuss the suitability of the method for Xeon Phi architecture and present our experience in the porting and optimization of the existing parallel Particle-in-Cell code PICADOR. Direct porting without code modification gives performance on Xeon Phi close to that of an 8-core CPU on a benchmark problem with 50 particles per cell. We demonstrate step-by-step optimization techniques, such as improving data locality, enhancing parallelization efficiency and vectorization leading to an overall 4.2× speedup on CPU and 7.5× on Xeon Phi compared to the baseline version. The optimized version achieves 16.9 ns per particle update on an Intel Xeon E5-2660 CPU and 9.3 ns per particle update on an Intel Xeon Phi 5110P. For a real problem of laser ion acceleration in targets with surface grating, where a large number of macroparticles per cell is required, the speedup of Xeon Phi compared to CPU is 1.6×.