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Detailed characterization of exoplanets has begun to yield measurements of their atmospheric properties that constrain the planets' origins and evolution. For example, past observations of the dayside emission spectrum of the hot Jupiter WASP-12b indicated that its atmosphere has a high carbon-to-oxygen ratio (C/O > 1), suggesting it had a different formation pathway than is commonly assumed for giant planets. Here we report a precise near-infrared transmission spectrum for WASP-12b based on six transit observations with the Hubble Space Telescope/Wide Field Camera 3. We bin the data in 13 spectrophotometric light curves from 0.84 to 1.67 μm and measure the transit depths to a median precision of 51 ppm. We retrieve the atmospheric properties using the transmission spectrum and find strong evidence for water absorption (7σ confidence). This detection marks the first high-confidence, spectroscopic identification of a molecule in the atmosphere of WASP-12b. The retrieved 1 σ water volume mixing ratio is between 10−5 and 10−2, which is consistent with C/O > 1 to within 2σ. However, we also introduce a new retrieval parameterization that fits for C/O and metallicity under the assumption of chemical equilibrium. With this approach, we constrain C/O to ${0.5}_{-0.3}^{+0.2}$ at 1σ and rule out a carbon-rich atmosphere composition (C/O > 1) at >3σ confidence. Further observations and modeling of the planet's global thermal structure and dynamics would aid in resolving the tension between our inferred C/O and previous constraints. Our findings highlight the importance of obtaining high-precision data with multiple observing techniques in order to obtain robust constraints on the chemistry and physics of exoplanet atmospheres.