Joao Felix's first goal for Chelsea was cancelled out by former Blues man Emerson Palmieri's strike to leave neither side in much a better position than they started.
Graham Potter's side started brightly and could have doubled their lead but for some wayward runs by their forward players before they faded and allowed West Ham back in.
Both sides will feel they could have won the game late on - West Ham through Tomas Soucek, who saw his header ruled out after Declan Rice had strayed offside and Chelsea after Conor Gallagher's shot struck the arm of the Czech midfielder.