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We report our discovery of observational evidence for the coherence between galaxy rotation and the average motion of neighbors. Using the Calar Alto Legacy Integral Field Area (CALIFA) survey data and the NASA-Sloan Atlas (NSA) catalog, we estimate the angular momentum vectors of 445 CALIFA galaxies and build composite maps of their neighbor galaxies on the parameter space of velocity versus distance. The composite radial profiles of the luminosity-weighted mean velocity of neighbors show striking evidence for dynamical coherence between the rotational direction of the CALIFA galaxies and the average moving direction of their neighbor galaxies. The signal of such dynamical coherence is significant for the neighbors within 800 kpc distance from the CALIFA galaxies with a confidence level of 3.5sigma, when the angular momentum is measured at the outskirt (Re
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