Chaves began his motorsport career in karting in 2004, where he remained active until 2009. He also made his debut in 2006 in Formula racing and finished ninth the Panam GP Series. In 2007, he competed in three Skip Barber Championships. The most successful he was in the Skip Barber Eastern Regional Series, in which he was charged with five wins from ten races runners behind Jordan Taylor. In addition, he started as a guest to a race to the Colombian Formula Renault, which he won. 2008 Chaves competed in the Formula BMW Pacific. Although he did not win a race, he finished fourth in the championship. In addition, he won the championship title of the Skip Barber Southern Regional Series and finished 14th in the Skip Barber National Championship. He also participated as a guest in two races in the Skip Barber Western Regional Series, which he won both, and three races of the American Formula BMW part. 2009 saw Chaves to Euro International in the American Formula BMW. He won five races and was at all the races on the podium. He finally sat down with 235 to 187 against his teammate Giancarlo Vilarinho, who scored the most victories by and decided the championship titles.
2010 left Chaves North America and moved to Europe in the Italian Formula 3 Championship, where he took up again for Euro International. He also changed for this season the racing license and ran as Americans. With a fourth place as best result he finished the season in tenth place in the championship. 2011 saw the launch Chaves for the Addax team in the GP3 Series. With a fourth place as best result he finished the season starting on the 19th place overall.
2012 Chaves returned back to North America. He drove for JDC Motorsports in the Star Mazda Series. He finished every race in the top 10 with two wins and ten podium finishes, he was behind Jack Hawksworth runner-up. He defeated his rival with 360 to 397 points. 2013 moved Chaves in the Indy Lights at Schmidt Peterson Motorsports. After a failure in the first race Chaves finished all the races in the top -4 and stand up on even getting on the podium. He won a race. With 449 to 460 points, he defeated his teammate Sage Karam and was runner-up.
- 2004-2009: Karting
- 2006 Panam GP Series ( course 9 )
- 2007: Skip Barber Eastern Regional Series ( 2nd place)
- 2007: Skip Barber National Championship ( 17th place )
- 2007: Skip Barber Southern Regional Series ( No. 47 )
- 2008: Formula BMW Pacific (4th place )
- 2008: Skip Barber Southern Regional Series ( Master )
- 2008: Skip Barber National Championship ( 14th place )
- 2009: American Formula BMW (Master)
- 2010: Italian Formula 3 ( 10th place )
- 2011: GP3 Series ( No. 19 )
- 2012: Star Mazda Series ( 2nd place)
- 2013: Indy Lights (2nd place)