Context: Cool stars, companions to compact objects, are known to show Li abundances which are high compared to field stars of the same spectral type, which are heavily Li depleted. This may be due either to Li production or Li preservation in these systems. Aims: Our aim is to measure the lithium isotopic ratio in the companion star of the neutron star X-ray binary Cen X-4. Methods: We use UVES spectra obtained in years 2000 and 2004 around the orbital quadratures. The spectra are analysed with spectrum synthesis techniques and the errors estimated with Monte Carlo simulations. Results: We measure A(Li) = 2.87±0.20 and ^6Li/^7Li = 0.12^+0.08_-0.05 at 68% confidence level. We also present updated system parameters with a refined determination of the orbital period and component masses i.e. 1.14±0.45 {M}_&sun; and 0.23±0.10 {M}_&sun; for the neutron star and companion, respectively. Conclusions: In our view the low level of ^6Li favours Li preservation scenarios, although Li production mechanisms cannot be ruled out. In the case of preservation, no Li is freshly created in the binary, but the tidally-locked companion has preserved its original Li by some mechanism, possibly inhibited destruction due to its fast rotation. Based on observations collected at ESO - Paranal in programmes 065-0447 and 073-0214.