Laser-induced fluorescence spectra of the B-X system of (KLi)-K-39-Li-7, recorded on a Fourier transform interferometer, have allowed 47 vibrational levels of the electronic ground state to be observed. The ground state energies have been fitted to a Dunham polynomial expansion, and also directly to a numerical potential curve. Both fits reproduce the data to within the experimental accuracy of measurement (0.005 cm(-1)).