His name started to appear in the chess columns in 1934 and in 1937 he won the first of many Belgian championships. He won the Belgian championships thirteen times between 1937 and 1959. He placed first at Beverwijk 1946 and by 1947 he was one of Europe's leading players, finishing first at the 1947 European Zonal tournament at Hilversum, tied for first place with Pirc at Teplice Sanov, tied for second at Venice. The next year O'Kelly de Galway finished first at São Paulo ahead of Eliskases and Rossetto.
He was awarded the IM title in 1950 and the GM title in 1956. He placed first at Dortmund 1951. He finished first at the round-robin Utrecht 1961 with 6.5 – 2.5 ahead of Karl Robatsch second with 6 points and Arthur Bisguier and Aleksandar Matanović tied for third and fourth with 5.5. O'Kelly was made an International Arbiter in 1962 and was the chief arbiter of the world championship matches between Tigran Petrosian and Boris Spassky in 1966 and 1969. In 1974 he was the arbiter for the Moscow Karpov–Korchnoi match.
He spoke French, Dutch, German, English, Spanish, and Russian well, and also some Italian. Chessmetrics puts his highest rating at 2644 in 1957, but his best ever performance was probably at Zagreb in 1955 where is performance rating was 2675 where he scored 10.5 – 7.5 against players whose average rating was 2619.
The following feisty little game shows how easy it can be for a GM to handle a "mere" IM.