We propose a semiempirical quantum chemical method, designed for the fast calculation of molecular Geometries, vibrational Frequencies and Non-covalent interaction energies (GFN) of systems with up to a few thousand atoms. Like its predecessors GFN-xTB and GFN2-xTB, the new method termed GFN0-xTB is parameterized for all elements up to radon (Z = 86) and mostly shares well-known density functional tight-binding approximations as well as basis set and integral approximations. The main new feature is the avoidance of the self-consistent charge iterations leading to speed-ups of a factor of 2-20 depending on the size and electronic complexity of the system. This is achieved by including only quantum mechanical contributions up to first-order which are incorporated similar to the previous versions without any pair-specific parameterization. The essential electrostatic electronic interaction is treated by a classical electronegativity equilibration charge model yielding atomic partial charges that enter the electronic Hamiltonian indirectly. Furthermore, the atomic charge-dependent D4 dispersion correction is included to account for long range London correlation effects. Formulas for analytical total energy gradients with respect to nuclear displacements are derived and implemented in the xtb code allowing numerically very precise structure optimizations. The neglect of self-consistent energy terms not only leads to a large gain in computational speed but also can increase robustness in electronically difficult situations because ill-convergence or artificial charge-transfer (CT) is avoided. The comparison of GFN0-xTB and GFN/GFN2-xTB allows dissection of quantum electronic polarization and CT effects thereby improving our understanding of chemical bonding. Compared to the most sophisticated multipole-based GFN2-xTB model (which approaches DFT accuracy for the target properties closely), GFN0-xTB performs slightly worse for non-covalent interactions and molecular structures, while very good results are observed for conformational energies. Vibrational frequencies are obtained less accurately than with GFN/GFN2-xTB but they may still be useful for various purposes like estimating relative thermostatistical reaction energies. Most exceptional is the fact that even relatively complicated transition metal complex structures can be accurately optimized with a non-self-consistent quantum approach. The new method bridges the gap between force-fields and traditional semiempirical methods with its excellent computational cost to accuracy ratio and is intended to explore the chemical space of large molecular systems and solids.