We report on the growth of one-dimensional (1D) chains of the prochiral quinacridone (QA) molecule on ultrathin KCl films on Cu(111) in ultrahigh vacuum. Using low-temperature scanning tunneling microscopy (STM), we observe straight homochiral 1D chains of QA molecules on one (1L), two (2L), and three (3L) atomic layer thick (100)-terminated KCl islands. The KCl films mostly consist of 2L-thick KCl islands delineated by long polar and short nonpolar edges. These 2L-thick KCl islands are topped by smaller one-atom-thick KCl islands or pits, which are delineated by nonpolar step edges. We find that QA chains can nucleate at these nonpolar step edges or on top of KCl terraces without assistance of step edges. In both cases, the longest straight QA chains observed grow along the KCl ⟨100⟩ directions or slightly rotated (typically less than 10∘) from them. Intermolecular distances ranging from 6.4 Å to 6.8 Å are measured for QA chains on KCl/Cu(111), which is compatible with hydrogen bonds between neighboring flat-lying QA molecules. These intermolecular distances being larger than the measured KCl lattice parameter (i.e., 6.21 Å at 78 K), QA chain growth on KCl/Cu(111) is incommensurate. Molecular arrangement models for the QA chains on KCl are proposed, based on the analysis of the STM images.