The invention relates to the fields of immunotherapy, molecular biology and recombinant nucleic acid technology. In particular, the invention relates to a TALEN-modified human primary cell comprising in its genome, a modified human T cell receptor alpha gene with an insertion comprising at least, from 5' to 3', a polynucleotide encoding a self-cleaving peptide, a chimeric antigen receptor, wherein the cell has undetectable cell-surface expression of the endogenous alpha beta T cell receptor as compared to a TCR positive control cell and expresses a receptor to target a pathological cell, use of said cell for treating a disease, including cancer. The invention further relates to methods for producing such a TALEN-modified cell, and to means for detecting such an engineered human primary cell or other genetically modified human primary cell obtained using alternative and/or additional rare cutting endonucleases.