Variability in patient response to anti-cancer drugs is currently addressed by relating genetic mutations to chemotherapy through precision medicine. However, practical benefits of precision medicine to therapy design are less clear. Even after identification of mutations, oncologists are often left with several drug options, and for some patients there is no definitive treatment solution. There is a need for model systems to help predict personalized responses to chemotherapeutics. We have microengineered 3D tumor organoids directly from fresh tumor biopsies to provide patient-specific models with which treatment optimization can be performed before initiation of therapy. We demonstrate the initial implementation of this platform using tumor biospecimens surgically removed from two mesothelioma patients. First, we show the ability to biofabricate and maintain viable 3D tumor constructs within a tumor-on-a-chip microfluidic device. Second, we demonstrate that results of on-chip chemotherapy screening mimic those observed in subjects themselves. Finally, we demonstrate mutation-specific drug testing by considering the results of precision medicine genetic screening and confirming the effectiveness of the non-standard compound 3-deazaneplanocin A for an identified mutation. This patient-derived tumor organoid strategy is adaptable to a wide variety of cancers and may provide a framework with which to improve efforts in precision medicine oncology.