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The helium absorption triplet at a wavelength of 10833 Å has been proposed as a way to probe the escaping atmospheres of exoplanets. Recently this feature was detected for the first time using Hubble Space Telescope (HST) WFC3 observations of the hot Jupiter WASP-107b. We use similar HST/WFC3 observations to detect helium in the atmosphere of the hot Neptune HAT-P-11b at the 4σ confidence level. We compare our observations to a grid of 1D models of hydrodynamic escape to constrain the thermospheric temperatures and mass loss rate. We find that our data are best fit by models with high mass loss rates of $\dot{M}\approx {10}^{9}\mbox{--}{10}^{11}$ g s−1. Although we do not detect the planetary wind directly, our data are consistent with the prediction that HAT-P-11b is experiencing hydrodynamic atmospheric escape. Nevertheless, the mass loss rate is low enough that the planet has only lost up to a few percent of its mass over its history, leaving its bulk composition largely unaffected. This matches the expectation from population statistics, which indicate that close-in planets with radii greater than 2 R⊕ form and retain H/He-dominated atmospheres. We also confirm the independent detection of helium in HAT-P-11b obtained with the CARMENES instrument, making this the first exoplanet with the detection of the same signature of photoevaporation from both ground- and space-based facilities.