Water is ubiquitous on earth, but we know little about the real-space motion of molecules in liquid water. We demonstrate that high-resolution inelastic x-ray scattering measurement over a wide range of momentum and energy transfer makes it possible to probe real-space, real-time dynamics of water molecules through the so-called Van Hove function. Water molecules are found to be strongly correlated in space and time with coupling between the first and second nearest-neighbor molecules. The local dynamic correlation of molecules observed here is crucial to a fundamental understanding of the origin of the physical properties of water, including viscosity. The results also suggest that the quantum-mechanical nature of hydrogen bonds could influence its dynamics. The approach used here offers a powerful experimental method for investigating real-space dynamics of liquids.