This paper presents the geometry optimization of a floating oscillating water column (OWC). The device consists of a floater pierced by a small thickness tube open at the bottom to the sea water and at the top to the OWC chamber. The dimensions of the floater and tube are optimized in order to maximize the wave energy extraction under certain geometric constraints. The formulation considers linear water wave theory. A boundary element method code is used to calculate the hydrodynamic coefficients. The floater and the water column are assumed to oscillate only in heave. The top of the water column is modeled as a piston. The compressibility effect of the air inside the chamber is accounted for. A Wells turbine with a linear characteristic curve is considered as a power take-off system. The system is modeled in the frequency domain, assuming two degrees of freedom. The power extraction from real sea waves is simulated through a stochastic model, using an energy spectrum and the wave climate conditions off the western coast of Portugal. The dimensions of the floating OWC are optimized using two distinct optimization algorithms. Results have shown that the diameter of the floater, the submerged length and the air chamber height have a large impact on the annual average power extraction.