Kilby received his bachelor of science degree from the University of Illinois at Urbana-Champaign in 1947 with a degree in Electrical Engineering. He obtained his master of science in Electrical Engineering from the University of Wisconsin-Milwaukee in 1950, while simultaneously working at Centralab in Milwaukee.
In the summer of 1958, Kilby was a newly employed engineer at Texas Instruments who did not yet have the right to a summer vacation. He spent the summer working on the problem in circuit design that was commonly called the "tyranny of numbers" and finally came to the conclusion that manufacturing the circuit components en masse in a single piece of semiconductor material could provide a solution. On September 12 he presented his findings to the management of Texas Instruments: he showed them a piece of germanium with an oscilloscope attached, pressed a switch, and the oscilloscope showed a continuous sine wave, proving that his integrated circuit worked and thus that he solved the problem. A patent for a "Solid Circuit made of Germanium", the first integrated circuit, was filed on February 6, 1959. In addition to the integrated circuit, Kilby also is noted for patenting the electronic portable calculator and the thermal printer used in data terminals. In total, he held about 60 patents.
From 1978 to 1985, he was Distinguished Professor of Electrical Engineering at Texas A&M University. In 1983, Kilby retired from Texas Instruments.
Kilby died June 20, 2005 when he was 81, in Dallas, Texas, following a brief battle with cancer.