Does undying trigger if a creature is killed while it already has a +1/+1 counter on it?

Undying reads: "When this creature dies, if it had no +1/+1 counters on it, return it to the battlefield under its owner's control with a +1/+1 counter on it." The condition "if it had no +1/+1 counters on it" is checked as the creature dies (i.e., as it last existed on the battlefield). If even a single +1/+1 counter was on it at that moment, undying will not trigger at all.

This is governed by CR 702.92a, which defines undying, and CR 603.4, which states that a triggered ability checks its intervening 'if' condition both when it would trigger and when it would resolve. Because the condition fails at the moment of death, the ability never even triggers.

It does not matter how the +1/+1 counter got there — whether it was placed by a previous undying trigger, by a +1/+1 counter effect like a proliferate, or any other source. As long as one +1/+1 counter is present when the creature dies, undying is suppressed.

Example: You control a Geralf's Messenger (which has undying). It died once before and returned with a +1/+1 counter. Your opponent targets it with a Lightning Bolt. When it dies this time, it already has a +1/+1 counter on it, so undying does not trigger and Geralf's Messenger goes to the graveyard and stays there.

If you can remove that +1/+1 counter before the creature dies — for instance with a Vampire Hexmage or a -1/-1 counter that cancels it out — then the creature would die with no +1/+1 counters and undying would trigger again.