Simply by hiring her, Hitchings provided Elion with an invaluable opportunity at a time when many of his contemporaries were unwilling to take female scientists seriously. As Elion said later, "He was one of these unusual people that didn't care whether it was a man or a woman, and gave us equal opportunity." Elion became friends with the entire Hitchings family and developed a very close relationship with George.

In the early years Hitchings was clearly the boss and Elion the assistant, but Hitchings allowed his staff considerable independence. "He is always willing to let people do the maximum that they are capable of doing," according to Elion. "I would read a lot, I would question why, I would have my own ideas, and he would encourage me to do that. Little by little, I began to have my own thoughts about what to make, I began to get assistants to help me.... He never said, 'OK, you've gone as far as you can go.'"

As time went on, Hitchings gave Elion more and more autonomy. "I think I had a little more patience to do the nitty-gritty kinds of things in the laboratory," Elion said, "but he had more insight, more appreciation of what these things all meant. We would have long talks about it. At the end of a long talk, you wouldn't really remember who said what and whose idea it was to do the next thing, which was great. You could never say, 'You told me to do this,' or 'I was the one who thought of it.' It was very much a meeting of the minds." During the 24 years they wrote papers together, not even their colleagues could tell say who had contributed what. Only following Hitchings' retirement from active research in 1967 was Elion completely on her own.

The Elion-Hitchings relationship was not completely without competitiveness. Elion herself admitted that Hitchings could be patronizing and that he tended to use "I" when referrring to their work while she used "we." Some observers have speculated that Hitchings was surprised to have his former assistant receive the Nobel Prize jointly with him and that the Prize thus strained their relationship. Members of Elion's family, however, doubt that this is true, emphasizing instead the longstanding deep mutual respect and admiration between the two scientists.