Chavarria and family moved between his birthplace (Los Angeles) and the ancestral home (Costa Rica) during his youth. He was in Costa Rica 1974–1980 and 1985–1990. After graduating high school in Costa Rica in 1990, Chavarria moved (by himself) to Houston, to further his education and follow his dream to become a broadcaster. He received his degree in radio/television from the University of Houston in 1996.
Chavarria began his career with the Houston Rockets in the 1995–96 basketball season, responsible for conducting interviews and for the halftime content. He was promoted to play-by-play announcer shortly thereafter.
Chavarria’s experience in broadcasting began as an intern with Telemundo in 1993. For three years he worked for Fox Sports Americas, and later Fox Sports World en Espanol, as a college basketball analyst, as well as a reporter for various sporting events. In 1996–97, Chavarria became the Rockets' Spanish radio color analyst. Midway through the season he was promoted to the Spanish play-by-play announcer.
Chavarria broadcast his 1600th NBA regular season game for the Rockets on March 28, 2017, when they faced the Golden St. Warriors. He has also broadcast over 100 playoff games, and over 125 pre-season games.
Chavarria also hosted “Contacto con los Astros”, a monthly television show that aired on FSN Houston from 2006 to 2007. In addition, Chavarria served as the English radio analyst and studio host for the Houston Comets of the WNBA in 2006. Chavarria was also one of the hosts of "Voces del Deporte" a daily local sports show that aired on ESPN Deportes Radio Houston from October 2010 to August 2011.
From March 2012 to December 2013, Chavarria hosted a daily local radio show "El Show de Adrian Chavarria" on ESPN Deportes, Radio Houston, 1180 AM. He has a presence on Facebook: www.facebook.com/HoustonRocketsVozenEspañol and his Twitter is : @ACROCKETS.