Basically, if Arsenal beats Newcastle and Everton hold Chelsea to a draw by these scorelines:
Arsenal 2-1 Newcastle Chelsea 0-0 Everton
... or any other result of adding one goal across the board (3-2, 1-1; 4-3, 2-2; etc) then Arsenal and Chelsea will finish level on points, goal difference and goals scored. Though Chelsea won both matches with Arsenal this year, that is not part of the tiebreak procedures. The next tiebreak is a one-match playoff. Actually, in most cases they wouldn't bother to break the tie, but the difference between third and fourth has something extra at stake: both are Champions League spots, but fourth has to go through a qualifying round while third goes right to the group stage.
I'm sure I won't be alone in saying head-to-head should probably factor into the tiebreaker, but I'm not going to complain if we get another match between two London rivals. The race between these two and Spurs for the last two Champions League spots has been cutthroat, really dramatic stuff. A humorous note also to me is that Chelsea have already played more games this year than any club in English history, adding one more right at the end seems fitting.