Marek Oliwa won medals twice in the Polish Youth Chess Championships in U20 age group: silver (Częstochowa 1992) and gold (Warsaw 1994; ahead of, among others, Marcin Kamiński, Bartłomiej Macieja and Bartosz Soćko).

In addition, he was a two-time medalist of Polish Blitz Chess Championship: silver (1996, Łuków[1]) and bronze (1998, Kędzierzyn-Koźle[2]).

Marek Oliwa twice appeared in the men's Polish Chess Championship finals (1995-1996), achieving the best result in 1995 in Warsaw, where he ranked in 11th place.

In the following year, he shared the 1st place (ahead of, among others, Stellan Brynell, Jacek Gdański and Emanuel Berg) in the next open in Gothenburg.

Marek Oliwa achieved the highest rating in his career on January 1, 1996, with a score of 2440 points, he was ranked 13th among Polish chess players.