Thompson was born in Los Angeles to Julie and Mychal Thompson. His mother was a volleyball player in college, and his dad was the first overall pick of the 1978 NBA draft. When Thompson was two, he and his family moved to Lake Oswego, Oregon, where he was childhood friends and Little League teammates with fellow future NBA star Kevin Love. At age 14, the Thompsons moved to Ladera Ranch, California, where Klay graduated from Santa Margarita Catholic High School in Rancho Santa Margarita in 2008. In his junior season he was named to the All-Area second team and to the Orange County third team. As a senior Thompson averaged 21 points per game and led SMCHS to a 30–5 record and a Division III State Championship appearance. During the state championship, Thompson set a state finals record with seven 3-pointers in a game. He was named Division III State player of the year, League MVP, first-team Best in the West, and an EA Sports Second Team All American.