The electronic and geometrical structures of the organic charge-transfer crystal of dimethylquaterthiophene (DMQtT) and tetrafluorotetracyanoquinodimethane (${\mathrm{TCNQF}}_{4}$) are calculated self-consistently from first principles using Car-Parrinello techniques. The calculated electronic charge transfer from the DMQtT molecule to the ${\mathrm{TCNQF}}_{4}$ molecule is 0.46e\ifmmode\pm\else\textpm\fi{}0.05e. This charge transfer is accompanied by a structural change in which the DMQtT molecule adopts a more quinoid geometry (compared to the aromatic structure of the neutral DMQtT molecule) and the ${\mathrm{TCNQF}}_{4}$ molecule becomes more aromatic. The electronic structure around the Fermi level is characterized by one-dimensional charge transfer states.