Nielsen was awarded the title of International Master by FIDE in 1991 and that of Grandmaster in 1994. He won the Danish Chess Championship five times: in 1996, 1999, 2001, 2003, and 2008. He played for Denmark in seven Chess Olympiads, three times on top board, with an overall result of 60.1% (+24−10=35). He won an individual gold medal on third board at Moscow 1994.