Patient-specific ex vivo models of human tumours that recapitulate the pathological characteristics and complex ecology of native tumours could help determine the most appropriate cancer treatment for individual patients. Here, we show that bioprinted reconstituted glioblastoma tumours consisting of patient-derived tumour cells, vascular endothelial cells and decellularized extracellular matrix from brain tissue in a compartmentalized cancer-stroma concentric-ring structure that sustains a radial oxygen gradient, recapitulate the structural, biochemical and biophysical properties of the native tumours. We also show that the glioblastoma-on-a-chip reproduces clinically observed patient-specific resistances to treatment with concurrent chemoradiation and temozolomide, and that the model can be used to determine drug combinations associated with superior tumour killing. The patient-specific tumour-on-a-chip model might be useful for the identification of effective treatments for glioblastoma patients resistant to the standard first-line treatment.