Heat the olive oil in a skillet over medium heat. Add the shallots and sauté for 3–5 minutes, until softened.
Stir in the fig jam, clementine juice, and bone broth. Cook gently for 1–2 minutes, stirring until combined.
Season the chicken breasts with salt and pepper and place them in the slow cooker.
Spoon the warm fig-shallot sauce over the chicken. Arrange the clementine slices and rosemary sprigs on top.
Cover and cook on low for approximately 6 hours, checking earlier if your slow cooker runs hot. The chicken is ready when a thermometer inserted into the thickest part, away from the bone, reaches 165°F.
Remove the rosemary stems. Serve the chicken with the shallots, clementine slices, and sauce spooned over the top.