Can Player B play a reaction to Shen when Player A plays Shen as a reaction to Blitzcrank, and does the reaction spell occur before Shen hits the field?

Ruling: Player B cannot play a reaction to Shen. Permanents (units and gear) exit the chain immediately after finalizing to be played and do not open priority windows.

Sequence:

• Player A plays Blitzcrank, it enters and triggers (choosing a target if available)
• Player B plays Shen in response to the trigger, it enters immediately without opening a priority window
• Player A now has a window to play actions/reactions in response to their own Blitzcrank trigger
• Blitzcrank trigger resolves

Nuances:

• Shen can only be played to Player B's own base or a battlefield they own (not to a battlefield where Player A is the attacker)
• Units do use the chain, but they are played immediately after finalizing, so it doesn't functionally matter for priority windows
• The Shen cannot be targeted by Blitzcrank's trigger because it's not in play yet when the trigger is put on the chain