  We study the branched holomorphic projective structures on a compact Riemann
surface $X$ with a fixed branching divisor $S\, =\, \sum_{i=1}^d x_i$, where
$x_i \,\in\, X$ are distinct points. After defining branched ${\rm
SO}(3,{\mathbb C})$--opers, we show that the branched holomorphic projective
structures on $X$ are in a natural bijection with the branched ${\rm
SO}(3,{\mathbb C})$--opers singular at $S$. It is deduced that the branched
holomorphic projective structures on $X$ are also identified with a subset of
the space of all logarithmic connections on $J^2((TX)\otimes {\mathcal
O}_X(S))$ singular over $S$, satisfying certain natural geometric conditions.
