Activate Troubled Healer by sacrificing Azorius Chancery.
When Azorius Chancery dies, Toph, Hardheaded Teach triggers, returning Azorius Chancery from your graveyard to the battlefield tapped.
When Azorius Chancery enters, it triggers, returning the artifact cast in step 1 from the battlefield to your hand, as it's a land due to Toph, the First Metalbender.
Resolve the Troubled Healer ability
Repeat.
This clever loop transforms a humble zero-cost artifact into a self-returning engine by leveraging Toph, the First Metalbender, whose static ability turns your noncreature artifacts into lands. With that foundation set, you cast your artifact to trigger Toph, Hardheaded Teacher, earthbending Azorius Chancery into a creature-land so it can be sacrificed to Troubled Healer's activated ability. When Azorius Chancery hits the graveyard, Toph, Hardheaded Teacher's safety-net trigger brings it right back to the battlefield tapped, prompting its own entry trigger to bounce the original artifact back to your hand. Because Toph, the First Metalbender makes that artifact count as a land, Azorius Chancery successfully returns it instead of a true land, letting you loop the entire sequence infinitely for every artifact, landfall, and death trigger you could ever want.