Very high quality p-type GaN thin films have been epitaxially grown on c-sapphire substrates by the MOCVD technique in a multiwafer rotating-disk reactor at 1040 degrees C with a GaN buffer layer of similar to 200 Angstrom grown at 530 degrees C. The undoped GaN films have a low n-type background carrier concentration of similar to 5 x 10(16) cm(-3) with an x-ray FWHM(GaN(0.002)) of 280 arc-sec across the 1 in. substrate. Biscyclopentadienyl magnesium (Cp(2)Mg) was used as the precursor Cp(2)Mg, the p-dopant. The Mg-doped GaN wafers retained an excellent surface morphology. In addition, after post annealing in N-2 ambient at similar to 700 degrees C for an hour, the Hall measurements show 6.7 x 10(17) to 5.2 X 10(18) cm(-3) carrier concentration depending on Cp(2)Mg flow rate, with a hole mobility of 10-20 cm(2)/V-s which is the best mobility for those hole concentrations reported in the literature to date.