HIV-1 protease (PR) is a major drug target in combating AIDS, as it plays a key role in maturation and replication of the virus. Six FDA-approved drugs are currently in clinical use, all designed to inhibit enzyme activity by blocking the active site, which exists only in the dimer. An alternative inhibition mode would be required to overcome the emergence of drug-resistance through the accumulation of mutations. This might involve inhibiting the formation of the dimer itself. Here, the folding of HIV-1 PR dimer is studied with several simulation models appropriate for folding mechanism studies. Simulations with an off-lattice Gō-model, which corresponds to a perfectly funneled energy landscape, indicate that the enzyme is formed by association of structured monomers. All-atom molecular dynamics simulations strongly support the stability of an isolated monomer. The conjunction of results from a model that focuses on the protein topology and a detailed all-atom force-field model suggests, in contradiction to some reported equilibrium denaturation experiments, that monomer folding and dimerization are decoupled. The simulation result is, however, in agreement with the recent NMR detection of folded monomers of HIV-1 PR mutants with a destabilized interface. Accordingly, the design of dimerization inhibitors should not focus only on the flexible N and C termini that constitute most of the dimer interface, but also on other structured regions of the monomer. In particular, the relatively high phi values for residues 23-35 and 79-87 in both the folding and binding transition states, together with their proximity to the interface, highlight them as good targets for inhibitor design.