On May 15, 1979, Norman Betros, Jr. received U.S. Patent No. D251,862 on a Round Chessboard or Checkerboard:

Outside of the novelty of the shape, presumably chess would be largely the same, with eight ranks and eight files, although things get curvier toward the edges. Circular chess has been known for centuries, played on a ring-shaped board, which requires a special arrangement of the pieces,