From Gordon Bell's book Computer Engineering - A DEC View of Hardware Systems Design: "DEC also never built a PDP-3, although one was designed on paper as a 36-bit machine. [...] In 1960 a customer (Scientific Engineering Institute, Waltham, Massachusetts) built a PDP-3. It was later dismantled and given to M.I.T.: as of 1974, it was up and running in Oregon."
According to Gordon Bell's oral history, the PDP-3 was designed on paper and sold to the Air Force Cambridge Research Lab, U.S. Hanscom field. Since DEC at the time didn't have the resources to build a new 36-bit machine, they persuaded the customer to take two PDP-1's instead.