Neurological disorder such as stroke can adversely affect one's weight-bearing symmetry leading to dysfunctional postural control. Recovery after stroke is facilitated through functionally-relevant neuroplastic modulation. Functionally-relevant cerebellum coordinates voluntary movements. Specifically, the dentate nuclei and lower limb representations (lobules VII-IX) of the cerebellum are involved in error-correction, crucial for postural control. It is postulated that cerebellar transcranial direct current stimulation (ctDCS) of the dentate nuclei and lobules VII-IX can modulate postural control in chronic stroke survivors. The objectives of this work were to (1) present a refined Virtual Reality (VR)-based balance training platform (VBaT) that can measure Center of Pressure (CoP) and (2) carry out a study to understand the implication of ctDCS stimulating the dentate nuclei (PhaseD) and lobules VII-IX (PhaseL) on the postural control of chronic stroke patients when they interacted with VBaT. Also, we investigated whether hemiplegic patients (with intact cerebellum) having Basal Ganglia (BG) infarction had any differential abilities to correct postural sway from those with no BG infarction (while shifting weight to the Affected side). Results of a single-session single-blind crossover study on randomized PhaseD and PhaseL stimulation (with an intermediate resting state bipolar bilateral ctDCS) on 12 chronic hemiplegic patients on separate days indicated differentiated findings (post stimulation) on CoP-related indices. We observed an incremental effect on one's postural control during PhaseD and inhibitory effect on the dentate nuclei during PhaseL. Clustering analysis showed that those with BG infarction demonstrated poor postural control and deficit in error correction ability irrespective of the ctDCS Phase.