The previously observed pressure-induced amorphization transition at 11 kbar [A.J. Schultz, U. Geiser, H.H. Wang, J.M. Williams, L.W. Finger and B.M. Hazen, Physica C 208 (1993) 277] was avoided and single-crystal X-ray data up to 28 kbar were obtained by replacing mineral oil with a hydrostatic alcohol mixture as the pressure medium in diamond anvil cell. The linear compressibilities of the crystallographic axes are remarkably isotropic given the two-dimensional nature of the structure. A full structure determination was performed at room temperature and 28 kbar with the use of X-ray data. It is noteworthy that, a novel structure feature, short interlayer H...H contacts through a hole in the anion layer, may account for the isotropic compressibilities. Electronic band structures calculated for the crystal structures of kappa-(ET)2Cu[N(CN)2]Cl at 1 bar, 3 kbar and 28 kbar show that this salt is a two-dimensional metal, and that the density of states at the Fermi level decreases gradually with increasing pressure.