The lithium (Li) abundance measured in the solar atmosphere is 140 times smaller than expected considering the proto-solar value. Furthermore, measurements of Li abundance made for many stars similar to the Sun reveal a large dispersion. These observations have defied the models of light element depletion for decades. We present a strong evidence for a correlation between Li depletion and the presence of planets. This result comes from the analysis of an unbiased sample of solar-analogue stars with and without planets detected, and for which precise spectroscopic stellar parameters were derived in an uniform way. Planet host stars are found to have typically only 1% of the primordial Li abundance while about 50% of the solar analogues without detected planets have on average ten times more Li. In addition, stellar evolutionary models were used to show that differences in stellar mass and age cannot be responsible for the observed correlation. These results suggest that the observed lithium difference is likely linked to some process related to the formation and evolution of planetary systems.