New measurements of the expansion rate of the Universe have plunged the standard model of cosmology into a severe crisis. In this letter, we propose a simple resolution to the problem that relies on a first order phase transition in a dark sector in the early Universe, before recombination. This will lead to a short phase of a New Early Dark Energy (NEDE) component and can explain the observations. We model the false vacuum decay of the NEDE scalar field as a sudden transition from a cosmological constant source to a decaying fluid with constant equation of state. The corresponding fluid perturbations are covariantly matched to the adiabatic fluctuations of a sub-dominant scalar field that triggers the phase transition. Fitting our model to measurements of the cosmic microwave background (CMB), baryonic acoustic oscillations (BAO, and supernovae (SNe) yields a significant improvement of the best-fit compared with the standard cosmological model without NEDE. We find the mean value of the present Hubble parameter in the NEDE model to be $H_0=71.4 pm 1.0 ~textrm{km}, textrm{s}^{-1}, textrm{Mpc}^{-1}$ ($68, %$ C.L.).
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