Bringing effective cancer therapy in the form of chimeric antigen receptor technology to untapped markets faces numerous challenges, including a global shortage of therapeutic lentiviral or retroviral vectors on which all current clinical therapies using genetically modified T cells are based. Production of these lentiviral vectors in academic settings in principle opens the way to local production of therapeutic cells, which is the only economically viable approach to make this therapy available to patients in developing countries. The conditions for obtaining and concentrating lentiviral vectors have been optimized and described. The calcium phosphate precipitation method was found to be suitable for transfecting high cell-density cultures, a prerequisite for high titers. We describe protocols for gradually increasing production from 6-well plates to P100 plates, T-175 flasks, and 5-layer stacks while maintaining high titers, >10 transducing units. Concentration experiments using ultracentrifugation revealed the advantage of lower centrifugation speeds compared to competing protocols. The resulting batches of lentiviral vectors had a titer of 10 infectious particles and were used to transduce primary human T lymphocytes generating chimeric antigen receptor T cells, the quality of which was checked and found potential applicability for treatment.