  The Hubble parameter inferred from cosmic microwave background observations
is consistently lower than that from local measurements, which could hint
towards new physics. Solutions to the Hubble tension typically require a
sizable amount of extra radiation $\Delta N^{}_{\rm eff}$ during recombination.
However, the amount of $\Delta N^{}_{\rm eff}$ in the early Universe is
unavoidably constrained by Big Bang Nucleosynthesis (BBN), which causes
problems for such solutions. We present a possibility to evade this problem by
introducing neutrino self-interactions via a simple Majoron-like coupling. The
scalar is slightly heavier than $1~{\rm MeV}$ and allowed to be fully
thermalized throughout the BBN era. The rise of neutrino temperature due to the
entropy transfer via $\phi \to \nu\overline{\nu}$ reactions compensates the
effect of a large $\Delta N^{}_{\rm eff}$ on BBN. Values of $\Delta N^{}_{\rm
eff}$ as large as $0.7$ are in this case compatible with BBN. We perform a fit
to the parameter space of the model.
