We present a molecular dynamics study of the single-particle dynamics of supercooled water confined in a silica pore. Two dynamical regimes are found. Close to the hydrophilic substrate molecules are below the mode coupling crossover temperature, TC, already at ambient temperature. The water closer to the center of the pore (free water) approaches upon supercooling TC as predicted by mode coupling theories. For free water the crossover temperature and crossover exponent γ are extracted from power-law fits to both the diffusion coefficient and the relaxation time of the late α region.