Peter Trefonas is a son of Louis Marco Trefonas, also a chemist, and Gail Thames. He was inspired by Star Trek and the writings of Isaac Asimov, and created his own chemistry lab at home.
Trefonas attended the University of New Orleans, receiving his Bachelor of Science in chemistry in 1980.
While an undergraduate, Trefonas earned money by writing video games for early personal computers. These included Worm, a clone of the 1976 arcade video game Blockade, and a clone of the arcade game Hustle (1977), which itself was based on Blockcade. Worm was the first of what would become many games in the snake video game genre for home computers. Trefonas also wrote a game based on Dungeons & Dragons.
Trefonas studied at the University of Wisconsin-Madison with Robert West, completing a Ph.D. in inorganic chemistry in late 1984. Trefonas became interested in electronic materials after working with West and chip makers from IBM to create organosilicon bilayer photoresists. His thesis topic was "Synthesis, properties and chemistry of organosilane and organogermane high polymers" (1985).