Add shallot to now-empty skillet and cook over medium heat until softened, about 2 minutes. Add flour and cook, stirring constantly, 30 seconds. Add broth, increase heat to medium-high, and bring to simmer, scraping pan bottom to loosen browned bits. Simmer rapidly until reduced to 3/4 cup, 3 to 5 minutes. Stir in any accumulated chicken juices; return to simmer and cook 30 seconds. Off heat, whisk in lemon juice, chives, and butter; season with salt and pepper. Spoon over chicken and serve immediately.

Makes about 3/4 cup