Charge hydration asymmetry (CHA)-a characteristic dependence of hydration free energy on the sign Of the solute charge-quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in Chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, similar to 50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA.