We obtain the perturbative QCD (PQCD) prediction for the leading twist deuteron form factor, treated as a pair of nucleons in nonrelativistic bound state. It is [lt]10[sup [minus]3] times experiment at [ital Q][sup 2]=4 GeV[sup 2], suggesting that PQCD is not relevant to the deuteron form factor at present values of [ital Q][sup 2], or that non-nucleon (e.g., hidden color'') degrees of freedom must be included for a correct description of the deuteron. The tree-level amplitude [similar to][ital eg][sup 10] and is the sum of several 10[sup 6] Feynman diagrams, making it an interesting case study in the behavior of perturbation theory.