The Human Immunodeficiency Virus Type 1 nucleocapsid 7 (NCp7) is a multi-functional protein formed by N-terminal and C-terminal domains surrounding two Zn-fingers, linked by a stretch of basic residues, which play a key role in the viral replication. We report the first NCp7 polarizable molecular dynamics (MD) study using the AMOEBA force field complemented by non-polarizable CHARMM simulations. Specifically, we compared the relative free-energy stability of two extreme conformations: a compact one having two aromatic residues from each finger, partially stacked, denoted A; and an unfolded one, with the two residues apart, denoted B. Each of these conformations had been previously experimentally advocated to prevail in solution. We compared their theoretical relative free-energy stability using accelerated MD sampling techniques (Steered MD and Umbrella Sampling) and showed that there was a low free energy difference between them. As A and B do not differ in stability by more than 1-1.5 kcal/mol, they should thus coexist in water solution reconciling earlier NMR experimental findings.