Place chicken breasts in an even layer in the bottom of a 4-6 quart crockpot.
Add potatoes and spread into an even layer as much as possible.
Combine butter, garlic, Italian seasoning, salt and pepper and pour over chicken and potatoes.
Cook on low for 2-4 hours, depending on your slow cooker (how hot it is and how wide it is — the deeper the food, the longer the cook time).
Add green beans for the last 30-60 minutes of cook time, depending on the texture you prefer.
Serve with remaining garlic butter in slow cooker.