We present the results of local density approximation (LDA) calculations for a novel Si endohedral system, Zr@Si20. We compute an LDA endohedral binding energy for this system of 11.2 eV with respect to an isolated Zr atom and the most stable Si20 isomer known. To understand the remarkable binding in this system, we compare the electronic structure of Zr@Si20 with that of the corresponding bare cluster and with other Si20 endohedral systems. We find that the bonding of all the endohedrals can be understood on the basis of a simple model previously used to explain endohedral bonding in small carbon fullerenes. Prospects for producing Zr@Si20 experimentally are discussed.