Born in Riga, he was champion of Latvia in 1955, 1956, 1957, 1960, 1961, 1963, 1964, and 1966. He also played in several Soviet Chess Championships, his best result coming in 1966, when he was equal third with 12/20. Gipslis played in the Sousse Interzonal of 1967, but did not advance to the Candidates' level. Perhaps his best tournament result was the Alekhine Memorial 1967 in Moscow, where he finished on 10/17, a point behind the winner Leonid Stein. His second place was shared with Milko Bobotsov and two World Champions, Vassily Smyslov and Mikhail Tal, ahead of two others, Boris Spassky and Tigran Petrosian, among a host of other strong players. His other outstanding tournament results include equal first at Bad Liebenstein 1963 with Lev Polugaevsky, and equal second at Budapest 1977 behind David Bronstein. Drink affected his performance in later years, but he continued to play right up to the year of his death .
He became an Grandmaster in 1967, and edited the Latvian chess periodical Šahs from 1963.
With the white pieces, he most frequently opened 1.e4. His repertoire with black was more varied. He is the eponym of the Gipslis Variation of the Sicilian Defence which he played the black side of several times in the 1960s: 1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 a6 5.Bd3 Nf6 6.O-O d6 7.c4 g6.