In the old days it came down to which letter of the club's name came first - I KID YOU NOT!
Bournemouth & Boscombe even changed their name to AFC Bournemouth; and West Brom thought of calling themselves simply "Albion".
That scenario could happen if the Gunners win by one goal at Newcastle and score one more goal than Chelsea manage in a draw at home to Everton.
That would make the clubs joint third and Arsenal and Chelsea would have to face a play-off for the automatic Champions League qualification spot.
The problem for the Premier League would be when to play such a match - Chelsea have an end-of-season tour to the USA to play friendlies against Manchester City next week, and then there are England friendlies on May 29 against the Republic of Ireland and then in Brazil on June 2.
1 Man Utd 88
2 Man City 78
3 Chelsea 72
4 Arsenal 70
5 Tottenham 69
Neither club would want the season to stretch into June but the play-off regulation is part of Premier League rules.
They state: "If at the end of the season... the question of qualification for other competitions cannot be determined because two or more clubs are equal on points, goal difference and goals scored, the clubs concerned shall play off one or more deciding league matches on neutral grounds, the format, timing and venue of which shall be determined by the board."