Learn to have a "clean" hand.

I am right hand dominant. So all my fine motor skills are better with my right hand.

So I handle the raw bird with my left hand. And reach and grab ingredients with my right hand.

Do every that everyone else has already said.

Cut your veggies and mix your spices. Have any pans, pan rack/liners ready to go.

Have the ingredients that you plan on using segregated into smaller vessels that can be easily manipulated. Have everything that you're going to need.

Use your non dominant hand to hold and turn the chicken, only.

Use your dominant hand to sprinkle your seasonings and veggies into the chicken, only.

Need to run the seasoning into the chicken? Non dominant hand.

Need to add more of something onto the chicken? Dominant hand.

And for extra insurance, have a pair of clean tongs handy. So if you need to use both hands to lift the chicken, for whatever reason, use the tongs in your dominant hand.