In cancer research and personalized medicine, new tissue culture models are needed to better predict the response of patients to therapies. With a concern for the small volume of tissue typically obtained through a biopsy, we describe a method to reproducibly section live tumor tissue to submillimeter sizes. These micro-dissected tissues (MDTs) share with spheroids the advantages of being easily manipulated on-chip and kept alive for periods extending over one week, while being biologically relevant for numerous assays. At dimensions below ~420 μm in diameter, as suggested by a simple metabolite transport model and confirmed experimentally, continuous perfusion is not required to keep samples alive, considerably simplifying the technical challenges. For the long-term culture of MDTs, we describe a simple microfluidic platform that can reliably trap samples in a low shear stress environment. We report the analysis of MDT viability for eight different types of tissues (four mouse xenografts derived from human cancer cell lines, three from ovarian and prostate cancer patients, and one from a patient with benign prostatic hyperplasia) analyzed by both confocal microscopy and flow cytometry over an 8-day incubation period. Finally, we provide a proof of principle for chemosensitivity testing of human tissue from a cancer patient performed using the described MDT chip method. This technology has the potential to improve treatment success rates by identifying potential responders earlier during the course of treatment and providing opportunities for direct drug testing on patient tissues in early drug development stages.