Can I legally respond to a Singularity by playing Janna to a battlefield?

Yes, you can legally respond to a Singularity by playing Janna, Savior to a battlefield.

Reasoning

1. Singularity starts a chain: When a player plays Singularity, it is placed on the chain. According to Rule 309.1, when a chain exists, the turn is in a Closed State.
2. Reaction timing: In a Closed State, only cards and abilities with the [Reaction] keyword can be played (Rule 309.1.a).
3. Janna's keyword: Janna, Savior possesses the [Reaction] keyword, which explicitly states: "Play any time, even before spells and abilities resolve, including to a battlefield you control."
4. Legality: Because Janna, Savior has the [Reaction] keyword, she can be played during the Closed State created by Singularity.

Sequence

1. Singularity is played and placed on the chain. The game state becomes Closed.
2. You play Janna, Savior as a reaction to Singularity.
3. Janna, Savior enters the board. Because she is a unit, she finalizes immediately (Rule 356.2).
4. Once Janna, Savior is in play, her "When you play me" triggered ability is placed on the chain on top of Singularity (Rule 356.3.c).
5. Players have an opportunity to play further reactions. If both pass, the chain resolves in LIFO (Last-In, First-Out) order:
   • Janna's ability resolves first.
   • Singularity resolves second.

Note: While Janna's "When you play me" ability can move an enemy unit, please be aware that per Rule 356.3.e.1, Singularity will still resolve even if its targets are moved or become illegal.

Note: I could not fully verify this ruling against the retrieved rules.