How Does Chains of Mephistopheles Work?
Chains of Mephistopheles doesn't form an infinite draw combo.

The main principle is this: when an event happens, we check all available replacement effects, and then we apply each of them just once. When Chains of Mephistopheles replaces your draw with an instruction to discard &amp; draw, that's not a new draw to which a replacement effect might be applied &mdash; it's just a modification to the original draw event, and Chains has already had its turn to change that event.

All of that happens specifically because Chains is a replacement effect, since it uses the language "If (thing would happen), (other thing happens) instead." If it was a triggered ability it would definitely go infinite.

Consider also that if this would lead to infinite draw, Anointed Procession would lead to infinite tokens, Winding Constrictor would lead to infinite counters, etc.

So what does it do? Chains of Mephistopheles is one of those very old cards that's complex enough it needs a flowchart to really understand. Magicjudge produced one here: