  Local Universe observations find a value of the Hubble constant $H_0$ that is
larger than the value inferred from the Cosmic Microwave Background and other
early Universe measurements, assuming known physics and the $\Lambda$CDM
cosmological model. We show that additional radiation in active neutrinos
produced just before Big Bang Nucleosynthesis by an unstable sterile neutrino
with mass $m_s=$ O(10) MeV can alleviate this discrepancy. The necessary masses
and couplings of the sterile neutrino, assuming it mixes primarily with
$\nu_{\tau}$ and/or $\nu_{\mu}$ neutrinos, are within reach of Super-Kamiokande
as well as upcoming laboratory experiments such as NA62 and DUNE.
