We present the results of a spectroscopic search for close binaries among horizontal branch (HB) stars in NGC6752. We used the ESO VLT-FORS2 instrument to obtain medium resolution (R=4100) spectra of 51 hot HB stars with 8000 < Teff < 32000 K during four consecutive nights. Eighteen of our targets are extreme horizontal branch (EHB) stars with Teff > 22000 K. Radial velocity variations were measured with cross-correlation techniques and we carefully evaluated the statistical and systematic errors associated with them. No close binary system has been detected among our 51 targets. The data corrected for instrumental effects indicate that the radial velocity variations are always below 15 km/s (3sigma level). From a statistical analysis of our results, we conclude that (at 95 confidence level) the fraction of binaries with a ~0.5 solar masses companion among EHB stars in NGC6752 is smaller than 20%. This empirical evidence sharply contrasts with what has been found for hot subdwarfs in the field, and opens new questions about the formation of EHB stars in globular clusters (and possibly in the field as well. Comment: 16 pages, 11 figures, A&A accepted