Born in Milan in 1986 Church drove a good first season in the Italian Formula 3 Championship, which he surpassed in 1987 with three wins in the first four races. In the championship, he had to at the end of the year but beaten by Enrico Bertaggia.
1988 Chiesa rose into the formula 3000. The first year was difficult and marked by many failures. Only one point for the championship could enter the Swiss. In 1989, he rose, won the race in Enna and finished second at Vallelunga. The championship he finished sixth.
In 1990, when the driver in the team of Paul Stewart, the son of Jackie Stewart, he achieved seventh place overall. However, his fourth consecutive season in Formula 3000 came a disaster. Although Chiesa had access to the best materials, the season ended without a single point in the championship.
Nevertheless Chiesa got a contract for 1992 in Formula 1, he signed with Fondmetal, the successor team of Osella and made his debut at the Grand Prix of Mexico. However, the time in Formula 1 was a failure. Chiesa could only thrice qualify for a Grand Prix and the failure rate was 100 %. Twice he retired after spinning off prematurely, in France he collided with Maurício Gugelmin.
The Formula 1 dream ended after only a year and Chiesa went to the USA. He drove the Champ Car inaugural race in 1993 in Surfers Paradise and played sports car racing for Riley & Scott.
After years of absence, the Swiss gave in 2007 at Le Mans team of Spyker a comeback. In 2008, he worked for the Dutch team and their Spyker C8 in the Le Mans Series and at the Sarthe circuit at the start. Both races ended in failure; 2007, there was an engine failure and the following year it was again a technical defect, which ended the trip early.