  Long-baseline neutrino oscillation experiments require external constraints
on $\sin^2\theta_{12}$ and $\Delta m_{21}^2$ to make precision measurements of
the leptonic mixing matrix. These constraints come from measurements of the
Mikheyev-Smirnov-Wolfenstein (MSW) mixing in solar neutrinos. Here we develop
an MSW large mixing angle approximation in the presence of heavy neutral
leptons which adds a single new parameter ($\alpha_{11}$) representing the
magnitude of the mixing between the $\nu_e$ state and the heavy sector. We use
data from the Borexino, SNO and KamLAND collaborations to find a solar
constraint appropriate for heavy neutral lepton searches in long-baseline
oscillation experiments. Solar data limits the magnitude of the non-unitary
parameter to $(1-\alpha_{11}) < 0.046$ at the $99\%$ credible interval and
yields a strongly correlated constraint on the solar mass splitting and the
magnitude of $\nu_e$ non-unitary mixing.
