Does Solemnity prevent undying from working?

Solemnity states that no player can place counters on creatures (or other permanents in some versions, but crucially on creatures). Undying, defined in CR 702.93, causes a creature that dies with no +1/+1 counters on it to return to the battlefield with a +1/+1 counter on it. If that counter cannot be placed, undying's effect is prevented.

When a permanent returns to the battlefield under undying, the game attempts to place a +1/+1 counter on it as a replacement-style trigger resolving. Solemnity creates a replacement effect (CR 614.1) that prevents any counters from being placed on creatures. Because the counter cannot be placed, the creature still returns to the battlefield — but with zero counters, meaning undying will no longer be locked out by a prior counter. However, since undying is a triggered ability that resolves by placing the counter, and Solemnity prevents that placement, the creature does come back but without the counter.

Importantly, the creature does still return to the battlefield — Solemnity does not stop the return itself, only the counter placement. However, since the creature comes back with no +1/+1 counter, undying's condition ("had no +1/+1 counters") is reset, so undying could theoretically trigger again the next time it dies. This creates a loop where the creature returns repeatedly each time it dies, as long as Solemnity is in play.

Concrete example: You control Geralf's Messenger (which has undying) and your opponent controls Solemnity. You attack and your opponent blocks and destroys Geralf's Messenger. Undying triggers, and it returns to the battlefield. When it tries to enter with a +1/+1 counter, Solemnity prevents the counter. The Messenger comes back with no counters — and will keep returning via undying every time it dies, as long as Solemnity remains.