The invention relates to methods and materials that can be used to product cytotoxic T cells that target cancer cells expressing the cancer-testis antigen NY ESO-1. Illustrative embodiments of the invention include peripheral blood stem cells transduced with a lentiviral vector that comprises a codon optimized TCR alpha and beta chain polypeptides specific for NY ESO-1. These gene-modified cells are useful, for example, in a hematopoietic stem cell transplantation setting to treat patients diagnosed with NY ESO-1 positive cancers.