Cichon played for Duke Blue Devils in the Atlantic Coast Conference of NCAA Division I. He finished the 2018 season with a 9-1 record, recording the most wins of any NCAA pitcher that year. His ERA of 1.96 was third in the NCAA behind teammate Andy Lollis, and Washington State's Keeley Sewell. He recorded his first complete game shutout on March 31, against Northwestern Wildcats, holding them to just 5-hits and 2 walks.
In the 2018 NCAA playoffs, Duke beat the Clemson Tigers, 3-1, with Chichon recording the win. He struck out 10 Clemson batters, throwing 80 strikes, and allowing just 9 hits and 1 walk, and earning player of the game. However, in the next series, Duke fell in two straight games to the eventual NCAA College World Series champions, Indiana Hoosiers.
With the NCAA season over, 23-year-old Cichon prepared for the Bull League draft. Cichon finished 2nd in NCAA Pitcher of the Year voting, in addition to having been selected to the NCAA All-Star Game.
The Arizona Cowboys selected Cichon first overall in the 2018 Bull League draft, inking a signing bonus of $3,960,000 on July 2, 2018. He was then sent to the A-level Yuma Hedgehogs where he had a rocky debut in a game the following day against the Lethbridge Raiders, throwing 5.0 innings and allowing 4 earned runs, 5 runs in total, on 9 hits.