If a player would draw a card except the first one they draw in each of their draw steps, that player discards a card instead. If the player discards a card this way, they draw a card. If the player doesn't discard a card this way, they mill a card.
Here’s what happens when Chains of Mephistopheles replaces a player’s draw: — If that player has at least one card in their hand, they discard a card and then draws a card. — If that player’s hand is empty, they put the top card of their library into their graveyard. The player doesn’t draw a card at all.