Bdtyktl

Is there a chess system where you can make players of differing skill levels compete against each other with an equal chance to win without using different chess variations?

This system should give good players and bad players a level playing field where both of them can win.

Yes.

The way I've done this in the past is to play a series of games with clocks starting with 10 minutes each on the clocks and then the rule for subsequent games that the winner of the previous game gets one minute less and the loser one minute more. This quickly stabilizes at a level where both players have good chances of winning.

Re-adding disclaimer as question edit was removed:
I'm answering meaningful version about different levels as there cannot exist equal 50/50 chance for unknown skill; it can be achieved theoretically, but than it would not be chess anymore - 2 color dice can be thrown with 50/50 chance, but in chess you cant make situation where newborn kid not knowing rules can have 50/50 chance Vs GM; even person just learned rules - you would need to use the method from @Brian Towers answer tweaking by second not minute to reach somewhat equal chance of GM mating or losing on time.
But...
Yes there is: It's handicap system - there are two main types of handicaps: time and material(as correctly pointed out in comments - material would take it out of current FIDE rules as chess variations where removed from their handbook few years ago).
for time typical tournaments are 10 min per game for both but 1 min shift for level (levels typically split around 2000 points each or by titles sometimes). for example 2 players with ~1800 rating would play in that tournament 5 min/game each; 2000 Vs 1800 would play 4 Vs 6 min 2200 Vs 1800 would have 3 Vs 7 2400 Vs 1800 would have 2 Vs 8 2600+ Vs 1800 would have 1 Vs 9 min; also 2600 Vs 2400 would play 4 Vs 6 min.
Also you can have material handicaps when someone starts a game missing some pawn or piece.