Transcranial direct current stimulation (TDCS) of primary motor cortex (M1) can transiently improve paretic hand function in chronic stroke. However, responses are variable so there is incentive to try to improve efficacy and or to predict response in individual patients. Both excitatory (Anodal) stimulation of ipsilesional M1 and inhibitory (Cathodal) stimulation of contralesional M1 can speed simple reaction time. Here we tested whether combining these two effects simultaneously, by using a bilateral M1-M1 electrode montage, would improve efficacy. We tested the physiological efficacy of Bilateral, Anodal or Cathodal TDCS in changing motor evoked potentials (MEPs) in the healthy brain and their behavioural efficacy in changing reaction times with the paretic hand in chronic stroke. In addition, we aimed to identify clinical or neurochemical predictors of patients' behavioural response to TDCS. There were three main findings: 1) unlike Anodal and Cathodal TDCS, Bilateral M1-M1 TDCS (1 mA, 20 min) had no significant effect on MEPs in the healthy brain or on reaction time with the paretic hand in chronic stroke patients; 2) GABA levels in ipsilesional M1 predicted patients' behavioural gains from Anodal TDCS; and 3) although patients were in the chronic phase, time since stroke (and its combination with Fugl-Meyer score) was a positive predictor of behavioural gain from Cathodal TDCS. These findings indicate the superiority of Anodal or Cathodal over Bilateral TDCS in changing motor cortico-spinal excitability in the healthy brain and in speeding reaction time in chronic stroke. The identified clinical and neurochemical markers of behavioural response should help to inform the optimization of TDCS delivery and to predict patient outcome variability in future TDCS intervention studies in chronic motor stroke.