Inhibitory control functions draw on a fronto-basal network with central cortical hubs at the right inferior frontal gyrus (IFG) and the pre-SMA. However, few neuropsychological studies investigated the role of brain regions in the left frontal cortex and some previous evidence from bilateral studies remained inconclusive. This study presents a systematic investigation with high-definition transcranial direct current stimulation (HD tDCS) in a focal 4 × 1 configuration, which was used to target the left IFG or the left dorsolateral prefrontal cortex (DLPFC) with 1-mA active or sham cathodal HD tDCS. Healthy participants were randomized into three groups. We analyzed performance in an adaptive stop-signal task to quantify inhibitory control before (baseline), during cathodal HD tDCS (on-line), and after cathodal HD tDCS (off-line) to either left IFG, left DLPFC, or sham. Results from 67 participants and Bayesian analyses indicated moderate evidence against an effect of cathodal tDCS (left DLPFC and left IFG compared with sham) regardless of timing, that is, on-line or off-line cathodal HD tDCS. The study results are examined in view of previous neuropsychological and neurostimulation studies with bilateral and unilateral cathodal tDCS in healthy and patient samples. Theoretically, our results are compatible with a right-lateralization of response inhibition functions and suggest a negligible role of the left frontal hemisphere in healthy participants, but more stimulation parameters can be still explored in the left hemisphere. In line with previous studies, right inferior frontal gyrus seems a more promising target to investigate or alleviate response inhibition with tDCS.