Place the chicken breasts in the bottom of the slow cooker.
Add the halved baby potatoes around the chicken.
Scatter the minced garlic over the chicken and potatoes.
Pour in the lemon zest, lemon juice, chicken broth, olive oil, oregano, salt, and pepper.
Cover and cook on low for 6 hours.
In the final 30 minutes, add the asparagus pieces and stir gently to combine.
Serve the chicken, potatoes, and asparagus together with the sauce from the slow cooker.