Answer by taking a quote from the following article:

James Harold Doolittle (December 14, 1896 - September 27, 1993) was an American aviation pioneer. A Reserve officer in the United States Army Air Corps, Doolittle was recalled to active duty during World War II. He was awarded the Medal of Honor for personal valor and leadership as commander of the Doolittle Raid, a bold long-range retaliatory air raid on the Japanese main islands, on 18 April 1942, four months after the attack on Pearl Harbor. The attack was a major morale booster for the United States, and Doolittle was celebrated as a hero.

Doolittle became acquainted with the field of space science in its infancy. He wrote in his autobiography, "I became interested in rocket development in the 1930s when I met Robert H. Goddard, who laid the foundation [in the US].... While with Shell [Oil] I worked with him on the development of a type of [rocket] fuel...." Harry Guggenheim, whose foundation sponsored Goddard's work, and Charles Lindbergh, who encouraged Goddard's efforts, arranged for (then Major) Doolittle to discuss with Goddard a special blend of gasoline. Doolittle piloted himself to Roswell, New Mexico in October 1938 and was given a tour of Goddard's workshop and a "short course" in rocketry and space travel. He then wrote a memo, including a rather detailed description of Goddard's rocket. In closing he said, "interplanetary transportation is probably a dream of the very distant future, but with the moon only a quarter of a million miles away--who knows!" In July 1941 he wrote Goddard that he was still interested in rocket propulsion research. The Army, however, was interested only in JATO at this point. Doolittle was concerned about the state of rocketry in the US and remained in touch with Goddard.  Shortly after World War II, Doolittle spoke to an American Rocket Society conference at which a large number interested in rocketry attended. The topic was Robert Goddard's work. He later stated that at that time "...we [the aeronautics field in the US] had not given much credence to the tremendous potential of rocketry.  In 1956, he was appointed chairman of the National Advisory Committee for Aeronautics (NACA) because the previous chairman, Jerome C. Hunsaker, thought Doolittle to be more sympathetic to the rocket, which was increasing in importance as a scientific tool as well as a weapon. The NACA Special Committee on Space Technology was organized in January 1958 and chaired by Guy Stever to determine the requirements of a national space program and what additions were needed to NACA technology. Doolittle, Dr. Hugh Dryden and Stever selected committee members, such as Dr. Wernher von Braun from the Army Ballistic Missile Agency, Sam Hoffman of Rocketdyne, Abe Hyatt of the Office of Naval Research and Colonel Norman Appold from the USAF missile program, considering their potential contributions to US space programs and ability to educate NACA people in space science.

Did he ever work with anyone famous during this time?
Dr. Wernher von Braun from the Army Ballistic Missile Agency,