Local Universe observations find a value of the Hubble constant H0 that is larger than the value inferred from the Cosmic Microwave Background and other early Universe measurements, assuming known physics and the ΛCDM cosmological model. We show that additional radiation in active neutrinos produced just before Big Bang Nucleosynthesis by an unstable sterile neutrino with mass ms= O(10) MeV can alleviate this discrepancy. The necessary masses and couplings of the sterile neutrino, assuming it mixes primarily with ντ and/or νμ neutrinos, are within reach of Super-Kamiokande as well as upcoming laboratory experiments such as NA62.