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Gillespie was born on a farm at Willard, Missouri, April 7, 1909. He was graduated Magna Cum Laude in Chemistry from Drury College, Springfield, Missouri, in1931. He taught Chemistry as a half time graduate student assistant for two years at Washington University, St. Louis, Missouri. In 1932, he invented, on paper, a helicopter with wing tip rocket propulsion. After visiting the patent office in Washington, he discovered that such a device had received a U.S. patent in 1871.

In 1933-34 Gillespie worked for the Western Cartridge Company in East Alton Illinois. As a research chemist, he developed the method of controlling crystal size in lead azide, thereby eliminating spontaneous detonation. This was later used in the manufacture of nearly all the explosive priming compositions in World War II. He also refined the purity and yield of tetracene, also used in primers.

From May 1934 until 1936 he worked as a research chemist for Monsanto Chemical Company, at the Rubber Service Laboratories, Nitro, West Virginia. He discovered the cause of the short-circuiting of hydrogen over-voltage during the electrolytic reduction of pyridine to piperidine, resulting in a saving of $500 per day thereafter. A turning point came in his career when he suffered from chemical poisoning. Gillespie stopped pursuing chemistry as a career.

He joined the American Interplanetary Society as Member #114. During the mid 1930s to early 1940s, he worked for Southwestern Bell Telephone Company, St. Louis, Missouri, as an engineer, lineman and cable splicer in the central office. He developed anti-corrosion techniques, which were adopted throughout the Bell System.

He was sent to the Bell Telephone Laboratories, Murray Hill, New Jersey, 1942-1945, where he developed the first megacycle ultra sound measuring system. Gillespie was the first to use the reciprocity method of calibrating electroacoustic transducer. He supervised the field development of the world's first sonar torpedo. Before concluding his employment at Bell Telephone Laboratories, he managed to patent the electroacoustic transducer and acoustic lens, in addition to, the electroacoustic transducer without housing reasonances.

From May 1946 until 1948 he worked at the General Electric Company, Schenectady, N.Y. for the Hermes Project. He also organized the Thumper anti-missile program where he contributed a number of advances in rocketry. In 1947 he made the original proposal for a joint operation among GE, JPL and Thiokol to build solid propellant rockets for the Army in a southern state. He initiated and supervised the design of the rocket. The proposal was later carried out in its original form, being the original major undertaking after the Army subsequently transferred its rocket activity to Redstone Arsenal. The rocket design was successful on the first test.

During the early 1950s, he moved to Aerojet-General Corporation, located in Azusa, California. There he worked with liquid fluorine as a rocket propellant in the form of aluminum borohydride. He was the first to recognize spin vibration in rocket motors; he also initiated the design of large rocket motors, which later were developed into the 1.6 million pound motor, Saturn V.

During the early to mid-Nineteen Fifties, he worked for Rocketdyne, located in Canoga Park, California, where he supervised 11 research programs and initiated some 20 important advances in rocket engines. He also personally observed tests of large rocket motors and was Project Engineer on the prototype of the 1.6 million-pound engine initiated during his employment at Aerojet. He introduced an improvement in the Altas combustion chamber that increased the thrust 8 per cent. Rocketdyne eventually got a contract to build six chambers, under a joint contract funded by the Navy and the Air Force.

Gillespie started work at JPL in about 1956. He was hired because of his experience with fluorine. Later, he supervised the theoretical machine calculation of specific impulses of a comprehensive list of some 350 liquid propellant combinations. He was able to reduce the large number of possible combinations to a few best choices. The complete list of oxidizers included two which had never been synthesized but which as a result of his report were subsequently synthesized by the methods he suggested, and found to match his predictions.

Gillespie eventually was Project Engineer at the JPL Edwards Test Station. There, Gillespie designed a 20,000-pound-thrust rocket test stand to burn chlorine trifluoride and hydrazine. He believed it was the first fully automated test stand ever built and the first rocket test stand to function flawlessly from the very first trial. Gillespie also introduced within his organization the most efficient rocket injector design, a 5,000-pound-thrust splash-plate injector, originally designed by Henry Stephens.

Four units were built and tested on the test stand at Edwards in series of tests extending over a period of one-year. Gillespie wanted to build nitrogen tetroxide/hydrazine combustion chambers for developing chlorine trifluoride motors.

A month before he left JPL, he assigned a draftsman the task of designing the feed system for such an injector. Before he had a chance to see the preliminary drawings, Jack E. Froelich, a division manager at JPL, saw it and ordered Gillespie's supervisor to remove him from all injector designs thereafter. He never saw the design. Froelich in 1957 fired Gillespie for an unauthorized meeting with Eisenhower's Science Advisor.

After leaving JPL in 1957, Gillespie joined Lockheed Missiles and Space Division, located in Sunnydale, California, from 1958-1963. While there, he initiated and supervised the design of a liquid-hydrogen/liquid -oxygen rocket.

Lockheed did not win the contract to build the rocket, but the design was the basis for the hydrogen rockets, which were built by other companies. Also, while at Lockheed Gillespie invented a practical solution of the "Kepler's Problem" of interplanetary trajectories. He also presented the first quantitative plans for manned interplanetary flights.

In 1963-1969 Gillespie was at NASA Headquarters, Washington, D.C., as head of space program planning where he prepared a proposal for a Comprehensive Space Transportation Program. His proposal was withdrawn from circulation when the Space Shuttle gained approval. He concluded his employment with NASA in 1969. Now retired, at age 91, Gillespie is fully occupied with research in cosmology and archaeology as well as writing a book titled "World Management."