  A recently developed nonperturbative chiral approach to describe the S=-1
meson-baryon reactions has been extended to investigate the near threshold $K^-
p \to \gamma \Lambda, \gamma \Sigma^0$ reactions. With the parameters governed
by chiral SU(3) symmetry, we show that the predicted branching ratios
$\Gamma_{K^- p \to \gamma \Lambda}/\Gamma_{K^- p \to all}$ and $\Gamma_{K^-p\to
\gamma \Sigma^0}/\Gamma_{K^- p \to all}$ are close to the experimental values.
The coupling with the $\eta$ channels, which was shown to be important in the
$S=-1$ meson-baryon reactions, is also found to be significant here. Our
results are consistent with the interpretation of the $\Lambda(1405)$ as a
quasi-bound meson-baryon state as found in other similar chiral approaches.
