He was born in Egio, Achaia and grew up in Athens, in the neighbourhood of Kallithea, as his family moved to the Greek capital in 1970.

Two years later he won the Greek Cadet Championship, under the guidance of FM Panagiotis Drepaniotis (1979–1981).

A relatively late starter, Grivas was taught how to play at a chess club when he was 13 years old.

[4] His greatest success was winning the Silver Individual Medal (on 3rd board) at the 33rd Chess Olympiad in 1998.

Other important successes were the Gold Individual Medal (on the 3rd board) at the European Team Championship in 1989, 4th place at the World Junior Chess Championship in 1985, 1st place at the 1987 Munich international tournament (320 participants), 11th individual place (on the 4th board) at the 32nd Chess Olympiad in 1996, qualification of his club (OAA “Iraklion”) to Europe's best 16 clubs in 1997 (European Club Cup) He scored the following at international tournaments: 3rd in Paris 1982, 1st in Cap d'Agde 1983, 2nd in Karditsa 1984, 3rd in Bucharest 1984, 2nd in Strasbourg 1985, 2nd in Munich 1986, 3rd in Xanthi 1991, 2nd in Gausdal 1993, 3rd in Reykjavík 1994, 2nd in Limassol 1997, 1st in Hellexpo-Sportexpo 2001.

He holds the titles of FIDE International Organizer (was a co-organizer of the 1999 European Youth Chess Championships in Litochoro Pierias with more than 1000 participants) and FIDE International Arbiter, titles that are awarded according to specific requirements and are not honorary.