Our concern is the computation of optimal shapes in problems involving(−Δ)1/2. We focus on the energyJ(Ω) associated to the solution uΩ of thebasic Dirichlet problem( − Δ)1/2uΩ = 1in Ω, u = 0 in Ωc. We show that regularminimizers Ω of this energy under a volume constraint are disks. Our proof goes throughthe explicit computation of the shape derivative (that seems to be completely new in thefractional context), and a refined adaptation of the moving plane method.