Chilavert made his debut as a football player with the team Sportivo Luqueño. He was trained by Modesto Sandoval. In 1989, he played for the Paraguayan national team for the first time. He later moved to Spain, where he played for Real Zaragoza. In 1988, whilst Chilavert played for Real Zaragoza, he stated that “the fans used to freak out” when he would come out with the ball at his feet and “scream at me to get back in goal. I’ve never stopped to think about what others are saying. I just rely on my abilities. Later on, I started to practice penalties and free kicks until they gave me the job for real”. Chilavert admitted to staying behind after training to practice 80 to 120 free kicks, which in his opinion was how he got better. After his time at Real Zaragoza, he moved to Argentina, where he played with Vélez Sársfield, helping them win the Primera División four times, as well as the Copa Libertadores and the Intercontinental Cup, both in 1994. In 1999, he became the first goalkeeper known to score a hat-trick in the history of professional football, while playing for Vélez against Ferro Carril Oeste, scoring all three goals through penalties. He also scored a free kick from behind the half-way line against River Plate. Whilst at Strasbourg, Chilavert played in the 2001 Coupe de France Final, in which his team beat Amiens SC on penalties, and Chilavert scored the winning penalty in the shootout.