  We consider a Gaudin model related to the q-deformed superalgebra
${\CU}_q(\mathfrak{osp}(1 | 2))$. We present an exact solution to that system
diagonalizing a complete set of commuting observables, and providing the
corresponding eigenvectors and eigenvalues. The approach used in this paper is
based on the coalgebra supersymmetry of the model.
