Watson and Crick won the Nobel Prize in 1962. James Watson, Francis Crick, and Maurice Wilkins shared that year's Nobel Prize in Physiology or Medicine for discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material.
The award recognized the 1953 proposal of DNA's double-helix structure. Watson and Crick built their model at the Cavendish Laboratory in Cambridge, drawing on X-ray diffraction evidence, chemical information, and the work of other researchers. Rosalind Franklin's DNA data, including Photo 51, were important to the discovery, although she was not included among the laureates.
The Nobel was awarded nine years after the landmark DNA paper. Franklin had died in 1958, and Nobel Prizes are not normally awarded posthumously. The prize was shared by three scientists because the committee recognized both the model-builders and Maurice Wilkins's contributions to the experimental DNA work.
A frequent mistake is to say that Watson and Crick alone received the prize. The year 1962 is correct, but Wilkins was the third laureate. The award was in Physiology or Medicine, not Chemistry.