De Broglie’s hidden-variables theory became known as the de Broglie-Bohm theory after David Bohm, who added to de Broglie’s theory and worked with him on it. However, it was still clearly non-local, and, as John Bell observed, “In fact the Einstein-Podolsky-Rosen paradox is resolved in the way which Einstein would have liked least” (meaning that the de-Broglie-Bohm theory is non-local). Bell went on to say that, notwithstanding the non-locality of the de-Broglie-Bohm theory, it would be interesting to see if you could prove that all hidden-variable theories are non-local.

Bell himself found the answer to his own question and published it in a new paper (Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics Physique Физика. 1 (3), 195–200 (1964). Reprinted in: Bell, J.S. Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press (1987)).