We study fully supersymmetric AdS(6) vacua of half-maximal N = (1,1) gauged supergravity in six space-time dimensions coupled to n vector multiplets. We show that the existence of AdS6 backgrounds requires that the gauge group is of the form G `' x G `' subset of SO(4,n) where G' subset of SO(3,m) and G `' subset of SO(1, n - m). In the AdS(6) vacua this gauge group is broken to its maximal compact subgroup SO(3) x H' x H `' where H' subset of SO(m) and H `' subset of SO(n - m). Furthermore, the SO(3) factor is the R-symmetry gauged by three of the four graviphotons. We further show that the AdS6 vacua have no moduli that preserve all supercharges. This is precisely in agreement with the absence of supersymmetric marginal deformations in holographically dual fi ve-dimensional superconformal field theories.