Relative humidity with respect to ice (RHi) is a major factor controlling the evolution of aircraft contrails. High-resolution airborne H2O measurements in and near contrails were made at a rate of 4.2 Hz using the novel water vapor mass spectrometer AIMS-H2O with in-flight calibration during the CONtrail, volcano, and Cirrus ExpeRimenT (CONCERT) 2011. Three 2 min old contrails were sampled near 11 km altitude. Independent of the ambient supersaturation or subsaturation over ice, the mean of the RHi frequency distribution within each contrail is shifted toward ice saturation. This shift can be explained by the high ice surface area densities with corresponding RHi relaxation times on the order of 20 s, which lead to the fast equilibration of H2O between the vapor and ice phase. Understanding the interaction of water vapor with ice particles is essential to investigate the life cycle of contrails and cirrus.