There are few cases in the history of physics in which a particle, theoretically predicted, has been detected repeatedly and not identified as such. This is what happened to the positron.
Paul Dirac showed in 1928 that it could be the case that a particle could have negative energy but a positive charge. It was in the same paper where he introduced his famous equation, a unification of quantum mechanics and special relativity and where the electron spin was used to explain certain phenomena. Dirac did not pose at this point the existence of an antielectron, but the solutions to his equation pointed in that direction.
In 1929 Dmitri Vladimirovich Skobeltsyn, the father of the “cosmic ray” concept, working with them in the Soviet Union attempted to explain the simultaneous appearance in the Wilson chamber of several relativistic particles. His were the first discussions of the cascade multiplication processes underlying high energy physics. He could not provide a thorough explanation of the experimental results as he did not identified the positron he had just measured.
Also in 1929, but at Caltech, Chung-Yao Chao was again using a Wilson chamber to study the scattering of gamma rays. He found some anomalous behaviours of electron-like particles but with trajectories that bended in the opposite direction under the influence of a magnetic field. No further research was done.
Frédéric and Irène Joliot-Curie, working in Paris independently also found the anomaly, but they interpreted it incorrectly assuming it was a proton.
Early in 1932 the positron was detected and identified as such in the Cavendish laboratory of the University of Cambridge by Patrick Blackett and Giuseppe Occhialini. But, typical of a Rutherford team, however, Blackett and Occhialini hold back his announcement until they had more solid evidence.
Also in 1932, at Caltech, Carl D. Anderson, under the supervision of Robert A. Millikan, began investigations into cosmic rays. In August he encountered unexpected particle tracks in his cloud chamber photograph that he correctly interpreted as having been created by a particle with the same mass as the electron, but with opposite electrical charge. In September that same year he published in Science “The apparent existence of easily deflectable positives”. The positron had been oficially discovered (and won Anderson a Nobel Prize in 1936).