SnO2 is a semiconductor with a wide optical bandgap (3.5 eV), which makes it an attractive transparent semiconducting oxide (TSO) for electronic and opto-electronic applications. At elevated temperatures it is, however, much more unstable than other TSOs (such as ZnO, Ga2O3, or In2O3). This leads to a rapid decomposition even under very high oxygen pressures. Our experiments showed that stoichiometric SnO2 does not melt up to 2100 °C, in contradiction to earlier published data. Bulk SnO2 single crystals, that could provide substrates for epitaxial growth, have not been reported so far. Hereby we report on truly bulk SnO2 single crystals of 1 inch diameter grown by physical vapor transport (PVT). The most volatile species during SnO2 decomposition is, in addition to oxygen, SnO, which is stable in the gas phase at high temperature and reacts again with oxygen at lower temperatures to form SnO2. We identified a relatively narrow temperature window, temperature gradients and a ratio of SnO/O2 for providing the best conditions for SnO2 single crystal growth. X-ray powder diffraction (XRD) proved the single SnO2 phase. Moreover, by selecting a suitable SnO/O2 ratio it was possible to obtain either n-type conductivity with electron concentrations up to 2 × 1018 cm−3 and electron mobilities up to 200 cm2 V−1 s−1, or insulating behavior. The crystals exhibited an optical absorption edge located at 330–355 nm, depending on the crystal orientation, and a good transparency over visible and near infrared (NIR) spectra.