A Swiss national born in Milan, Chiesa made a solid start in Italian F3 in 1986, but was hampered by problems with his VW engine. For 1987 he was well prepared, surging out of the blocks with three wins in the first four races, but his season then tailed off and Enrico Bertaggia pipped him to the title. Stepping up to F3000, Chiesa struggled in 1988, notching just a single point, but things improved the following year, Andrea winning at Enna and finishing second at Vallelunga to claim sixth place in the final points standings.
His third season in the formula, with Paul Stewart Racing, was much the same and he managed seventh in the final table, but his fourth, in 1991, was an utter disaster, Chiesa failing to score even a point with a competitive Reynard. But such are the vagaries of motor racing that when the Formula 1 team line-ups were confirmed for 1992, Andrea was confirmed at Fondmetal. He was out of his depth and his record of three starts (two spins, one collision) and seven DNQs tells the sorry tale. For Chiesa the F1 dream was over, but he briefly reappeared in 1993, racing in the opening round of the Indy Car series in Surfers Paradise, Australia.
After three years away from the sport Chiesa briefly returned to the track in a Riley & Scott with Alex Caffi at Laguna Seca in 1996. The partnership was successfully renewed in 1998 when the pair scored a couple of third places in the ISRS series at the Paul Ricard and Le Mans (Bugatti) rounds. In recent years (most recently 2003) Andrea has raced a Porsche in the FIA GT Championship.
- 1982: Karting in the Swiss National Championship Class B.
- 1983: Swiss National Champion Class B
- 1984: Karting, Swiss National Championship. 3rd European Championship.
- 1985: Selected for the Marlboro test in F.3000. F3 with the Trivellato Team.
- 1986: Italian F3 Championship. Team Trivellato Dallara 386/VW, 10th in the Championship with 1 pole position.
- 1987: Italian F3 Championship. Euroracing team Dallara/Alfa Romeo. 2nd in the Championship with 3 victories and 3 pole positions.
- 1988: Intercontinental Formula 3000. Team Motorsport COBRA.
- 1989: Intercontinental Formula 3000. Team Roni Motorsport Q8 Ford Team. Reynard Cosworth. 6th in the Championship with one win.
- 1990: Intercontinental Formula 3000. With Team Paul Stewart. 2 second places 3 thirds finishing 6th in the Championship.
- 1991: Intercontinental Formula 3000. With the Apomatox Team. Budget prob
- 1992: Formula 1 with Fondmetal. 10 races, qualified on three occasions: Mexico, Spain and France.
- 1993: Indycar with Euromotorsport team.
- 1996: FIA GT Championship with Callaway-Corvette GT2. Finished 4th at the 1000km of the Suzuka.
- 1997: World Sports-car Championschip with Riley & Scott.
- 1998: ISRS European Sports Prototype Championship, Riley & Scott for the Team Target 24.
- 2000: 24h of the Nurburgring with a BMW M3 and 24h of Spa Francorchamps finishing 3rd. Sports Racing World Cup with the Team R&M Riley & Scott Judd.
- 2001: FIA GT Endurance Championship with Porsche GT3. Teams: Freisinger and Orlando. Best result 2nd at the 24h of Spa.
- 2002: FIA GT endurance championship. Teams: Loris Kessel Racing, Scuderia Sant Ambroeus. Car: Ferrari Modena 360 GT. Best result: 1st in class in the 24h of Spa.
- 2003: 24h of Daytona 24 with a Porsche GT3 RS Seikel. 12h of Sebring 2nd in GT class with Seikel Team Porsche GT3 RS.