Since early in 2003, several experiments have presented evidence for the existence of a positive strangeness baryon state of mass around 1540 MeV/c{sup 2} and width <8 MeV, the {Theta}(1540), which decays to K{sup +}n and K{sup 0}p. Such a state has minimum quark content udud{bar s} and consequently has been interpreted as the S = +1 member of the anti-decuplet of pentaquark states proposed by Diakonov et al. Subsequently, the NA49 experiment presented evidence for the S = -2 member of the anti-decuplet, the {Xi}{sub 5}(1860){sup --}, but this has yet to be observed in any other experiment. Results from the search for the production of the {Theta}(1540) memember of the anti-decuplet of pentaquark states using data from e{sup +}e{sup -} collisions obtained with the BABAR detector at the PEP-II Collider are presented. No signal is observed, and cross section limits for the {Theta}(1540) are given; these prove to be well below the cross section values for ordinary baryons of similar mass. In addition, a search has been carried out for the electroproduction of the {Theta}(1540) in the material of the BABAR detector. Event selection procedures are discussed in detail, the results of this search are presented, and are …