For a 2D chess game you may use the
Graphics View Framework | Qt Widgets 5.6[
^].
The chess board can be then drawn on the background layer of the
QGraphicsScene Class | Qt Widgets 5.6[
^]. Designing the board should be no problem. Just draw the 64 rectangles filled with alternating colours.
The pieces can be implemented using the
QGraphicsItem Class | Qt Widgets 5.6[
^] when drawn by code. If the pieces has been created as bitmap images, use the
QGraphicsPixmapItem Class | Qt Widgets 5.6[
^].
The latter option should be the simpler one. You might search the web for existing chess pieces (but be aware of image copyrights if you want to publish your program).