This paper proposes a novel tree decomposition based side-chain assignment algorithm, which can obtain the globally optimal solution of the side-chain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is $O((N+M)n_{rot}^{tw+1})$ where $N$ is the number of residues in the protein, $M$ the number of interacting residue pairs, $n_{rot}$ the average number of rotamers for each residue and $tw (=O(N^{\frac{2}{3}}\log{N}) )$ the tree width of the residue interaction graph. Based on this algorithm, we have developed a side-chain prediction program SCATD (Side Chain Assignment via Tree Decomposition). Experimental results show that after the Goldstein DEE is conducted, $n_{rot}$ is around 3.5, $tw$ is only 3 or 4 for most of the test proteins in the SCWRL benchmark and less than 10 for all the test proteins. SCATD runs up to 90 times faster than SCWRL 3.0 on some large proteins in the SCWRL benchmark and achieves an average of five times faster speed on all the test proteins. If only the post-DEE stage is taken into consideration, then our tree-decomposition based energy minimization algorithm is more than 200 times faster than that in SCWRL 3.0 on some large proteins. SCATD is freely available for academic research upon request.