If you're going to grill the chicken, turn the grill to medium heat and let it warm.
In a bowl, mix together sour cream, lemon juice and seasonings.
In a pan on the stove, heat chicken broth to warm. This is especially important if you're using chicken broth that has been in the refrigerator. Be careful not to let it boil or even simmer. Cook on low heat for about 3-4 min.
Add the chicken to the grill and cook for about 3-4 minutes on each side with the grill closed. Make sure the internal temperature is at 165 degree before removing it. Times will truly vary based on the thickness of the chicken breast.
Slowly begin whisking the chicken broth into the sour cream mix. pour in a little at a time and continuously and vigorously mix it until everything is well combined.
Plate the chicken immediately when done and add the chive souce to the top. Add on additional chives, salt and pepper and chive flowers as desired.