We have developed a model atom for Cu with which we perform statistical equilibrium computations that allow us to compute the line formation of \ion Cui lines in stellar atmospheres without assuming Local Thermodynamic Equilibrium ( LTE ) . We validate this model atom by reproducing the observed line profiles of the Sun , Procyon and eleven metal-poor stars . Our sample of stars includes both dwarfs and giants . Over a wide range of stellar parameters we obtain excellent agreement among different \ion Cui lines . The eleven metal-poor stars have iron abundances in the range -4.2 \leq [ Fe / H ] \leq - 1.4 , the weighted mean of the [ Cu/Fe ] ratios is -0.22 dex , with a scatter of -0.15 dex . This is very different from the results from LTE analysis ( the difference between NLTE and LTE abundances reaches 1 dex ) and in spite of the small size of our sample it prompts for a revision of the Galactic evolution of Cu .