Boris Čukvas began his water polo career with PVK Jadran in 1949 and stayed with them through 1960. During that time, he won the Yugoslav Water Polo Championship in 1958 and 1959, as well as a silver medal at the 1958 European Championships. He was also a reserve with the national team at the 1960 Rome Olympics, although he did not see any playing time in Yugoslavia’s fourth-place finish. He then switched to VK Partizan and won four consecutive national titles (1963-1966) prior to his retirement in 1967. He also picked up an additional European silver medal in 1962, and took part in the Mediterranean Games in 1959 and 1961.