Hv1 is a voltage-gated proton channel whose main function is to facilitate extrusion of protons from the cell. The development of effective channel blockers for Hv1 can lead to new therapeutics for the treatment of maladies related to Hv1 dysfunction. Although the mechanism of proton permeation in Hv1 remains to be elucidated, a series of small molecules have been discovered to inhibit Hv1. Here, we compute relative binding free energies of a prototypical Hv1 blocker on a model of human Hv1 in an open state. We use alchemical free energy perturbation techniques based on atomistic molecular dynamics simulations. The results support our proposed open state model, sheds light on the preferred tautomeric state of the blocker that binds Hv1, and lays the groundwork for future studies on adapting the blocker molecule for more effective channel blocking.