We have coupled hybrid quantum mechanics (density functional theory; Car-Parrinello)/molecular mechanics molecular dynamics simulations to a grand-canonical scheme, to calculate the in situ redox potential of the Cu(2+) + e(-) --> Cu(+) half reaction in azurin from Pseudomonas aeruginosa. An accurate description at atomistic level of the environment surrounding the metal-binding site and finite-temperature fluctuations of the protein structure are both essential for a correct quantitative description of the electronic properties of this system. We report a redox potential shift with respect to copper in water of 0.2 eV (experimental 0.16 eV) and a reorganization free energy lambda = 0.76 eV (experimental 0.6-0.8 eV). The electrostatic field of the protein plays a crucial role in fine tuning the redox potential and determining the structure of the solvent. The inner-sphere contribution to the reorganization energy is negligible. The overall small value is mainly due to solvent rearrangement at the protein surface.