Robert Gwaze was born in Harare, Zimbabwe in 1982. He learned how to play chess at the age of 9.
In 1997, at the age of 15, he won the Zimbabwe National Championship, the youngest player to do so.
In 1998, he won the African Junior Championship, held in Kenya, and was awarded the International Master (IM) title.
In 1999, he won the African Junior Championship again.
In 2000, he played Board 1 for Zimbabwe at the chess Olympiad in Istanbul.
In 2002, he won all 9 of his games on board one for a 100% score at the 2002 Chess Olympiad in Bled. He won the individual gold medal for best board 1. The only other person to score 100% on Board 1 playing at least 9 games was world champion Alexander Alekhine at the 1930 Hamburg Olympiad.
In 2007, he won the African Chess Championship in Windhoek, Namibia.
In 2008, he represented Africa at the world chess championships in Moscow.
In 2011, Gwaze (2434) lost in the first round of the 2011 World Cup to Ruslan Ponomarov (2764). Gwaze drew one game and lost one game to Ponomarov.