A high-resolution scanning superconducting quantum interference device microscopy study of tetragonal single-layer Tl2Ba2CuO6+delta films, deposited on tricrystal SrTiO3 substrates, demonstrates the effect of spontaneously generated half flux quanta. This observation shows that in addition to YBa2Cu2O7, the order parameter symmetry in Tl2Ba2CuO6+delta is consistent with that of a d(x?2-y)(2) pair state. This result also rules out any bilayer or twinning effects and any pairing that is incompatible with the fourfold rotational symmetry as in the Tl2Ba2CuO6+delta superconducting system.