Place the chicken breasts into the slow cooker.
Add the diced onion and minced garlic on top of the chicken.
Whisk together the Dijon mustard, honey, and melted salted butter until smooth, then pour over the chicken.
Season with salt and pepper to taste and tuck the rosemary sprig into the sauce.
Cover and cook on high for 3–4 hours (about 240 minutes) or until the chicken is fully cooked and tender.
Discard the rosemary sprig. Remove the chicken, shred it with two forks, then return the shredded chicken to the sauce and stir to combine.
Stir in a few dried chives for color if desired and keep warm until ready to serve.
Serve the honey mustard chicken over rice.