+1 to mfg for the crock pot suggestion. That is how we make it.
To expand a bit, we do not put the cheese on top. We find that it hardens into a skin once it cools a bit, making it very difficult to dip anything into it.
Instead we combine the shredded cheese with all the other ingredients at once in the crock pot.
We do cook the chicken separately, boiled usually. The key to a consistent texture there is to finely shred the chicken in a food processor rather than fork or hand shredding, as larger or longer pieces of chicken make for a lot of broken chips.
We actually just made a batch of this yesterday using boneless skinless thighs rather than breasts and even with the higher fat content we had no problems with separation or oil run off.
I also want to add that we have tried putting larger chicken pieces in the dip and then using an immersion blender to smooth out the whole mix. I don't recommend it. The chicken doesn't end up uniform in size, and when hot the dip combines easily with minimal stirring so you don't gain anything by such rigorous blending.
I want to add one more thing about doing this in a crock pot: don't let it sit too long on its own with the crock pot on. It will burn. Even on the lowest setting, the parts that are touching the sides will scorch. If it happens a little bit, you can stir it in and it's not so bad, but it's definitely not at its best that way.
This dip reheats really well either in the crock pot or in a microwave, so don't be afraid to let it cool and reheat it.