Vukic only started to play chess as a young man, having been occupied with other sports during his teenage years.
[2] Earning the title International Master in 1967 and Grandmaster in 1975, he first won the Yugoslav Chess Championship (SFRY) in 1970 and added further victories in 1971 and 1974.
In the midst of the Balkan war hostilities (1992–1995), it was not uncommon for passionate chess players, like Vukić, to ignore the dangers and carry on playing in scheduled competitions.
[6][7] Since then, he has remained fairly active as a tournament player and continues to record the occasional win, such as his shared first place at Hotel Opatija (Rijeka) in 2002.
At the European Team Chess Championship, he played in 1970 and in 1980, taking home an individual bronze medal on the second outing.