Let $S$ be a closed, orientable surface of genus at least $2$ . The space ${\mathcal T}_H\times {\mathcal ML}$ , where ${\mathcal T}_H$ is the “hyperbolic” Teichmüller space of $S$ and ${\mathcal ML}$ is the space of measured geodesic laminations on $S$ , is naturally a real symplectic manifold. The space ${\mathcal CP}$ of complex projective structures on $S$ is a complex symplectic manifold. A relation between these spaces is provided by Thurston's grafting map ${\rm Gr}$ . We prove that this map, although not smooth, is symplectic. The proof uses a variant of the renormalized volume defined for hyperbolic ends