  The static $B^{*}B\pi$ coupling, $\hat{g}_\chi$, a low energy constant in the
leading order heavy meson chiral Lagrangian, is determined using $N_\mathrm{f}
= 2$ lattice QCD. We use CLS ensembles with lattice spacings and pion masses
down to $a = 0.05\mathrm{fm}$ and $m_{\pi}=270\mathrm{MeV}$, and perform
combined continuum and chiral extrapolations of our results which have a much
better accuracy than previous numbers in the literature. As a by-product, we
determine the coupling between the first radial excitations in the $B$ and
$B^{*}$ channels ($\hat{g}_{22}$). Accounting for all uncertainties, which are
dominated by the chiral extrapolation, we obtain $\hat{g}_\chi = 0.492(29)$,
while $\hat{g}_{22}$ is somewhat smaller. The comparison to a precise quenched
computation suggests that there is little influence by the sea quarks and
$\hat{g}_\chi$ will not change much when a dynamical strange quark is included.
