In July 2008, well KJ-39 encountered magma at 2571 metres below the surface while drilling into the geothermal system within the Krafla central volcano, north-eastern Iceland. The magma was returned to the surface as quenched glass along with a resorbed mineral assemblage consisting of bytownite with some anorthite and augite with minor pigeonite and orthopyroxene lamellae. In June 2009, the better-known IDDP-1 well, located 2.5 km north of KJ-39, also intercepted rhyolitic melt and partially molten felsite rich in quartz, plagioclase and alkali feldspar. Because of the proximity of the two drill holes, I investigate whether the magma encountered in KJ-39 is from the same source as IDDP-1. This will have important implications for the dimensions of the magma chamber and thus future geothermal drilling operations. Major elements, S, Cl and F have been measured in KJ-39 glass chips using electron probe micro-analysis (EPMA) and H2O and CO2 have been measured using Fourier-transform infrared spectroscopy (FTIR). The KJ-39 chips have a striking range in composition, from andesitic to rhyolitic (SiO2 58-75 wt%), the H2O content ranges from 0.64-3.02 wt% with some samples showing evidence of partial or total hydration and CO2 measurements range from 5- 40 ppm, although most measurements were masked by atmospheric CO2. S contents range from below detection to 1373 ppm and show a strong negative correlation with SiO2, as does F, while Cl shows a positive correlation with SiO2. Based on the chemistry and petrology of the KJ-39 samples, there is evidence for formation of a high-SiO2 rhyolite by partial melting of hydrated basalt, while the andesitic and dacitic glass compositions presented here suggest partial melting of a more mafic source, an andesite, likely melted by the same heat source. When this mechanism for formation is compared with that for IDDP-1 both are to some degree formed by the partial melting of hydrated basalt. The wide range of glass compositions in the KJ-39 sample compared to IDDP-1 suggests that the two melts are not derived from the same source; however, the proximity of the two wells indicates that melting could have been driven from the same heat source. The evidence provided by this study for partial melting processes producing high-SiO2 rhyolites in basaltic environments, such as Krafla, shows that this process could be more common than previously considered. The wider Krafla region could, therefore, have more of these felsic melt pockets, the peripheries of which would be ideal targets for geothermal exploration and exploitation.