We present the design and use of an ultrathin, stretchable sensor system capable of conformal lamination onto the skin, for precision measurement and spatial mapping of levels of hydration. This device, which we refer to as a class of 'epidermal electronics' due to its 'skin-like' construction and mode of intimate integration with the body, contains miniaturized arrays of impedance-measurement electrodes arranged in a differential configuration to compensate for common-mode disturbances. Experimental results obtained with different frequencies and sensor geometries demonstrate excellent precision and accuracy, as benchmarked against conventional, commercial devices. The reversible, non-invasive soft contact of this device with the skin makes its operation appealing for applications ranging from skin care, to athletic monitoring to health/wellness assessment.