Zest the lemon and set the zest aside. A microplane grater is best for this, but if you don't have one, use a vegetable peeler to peel off the lemon rind (be sure not to press too hard, you don't want the bitter white layer underneath). Then chop the strips of rind as finely as possible.
Halve the lemon and squeeze out the juice until you have 1/4 cup. (My favorite trick? I don't have a juicer so I set a small mesh sieve over a measuring glass, stab the cut side of the lemon with a fork, aim the cut side down over the sieve and squeeze and rotate the lemon while twisting the fork until I gouge out every last drop of juice.)
Whisk together the coconut milk, lemon juice, ½ salt and ¼ pepper.
Pat the chicken breasts dry and trim any excess fat. Sprinkle both sides with the 1½ teaspoons salt, ¾ teaspoon pepper and Italian seasoning.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Sear the chicken breasts for about 4-5 minutes per side. They might not be cooked all the way through yet which is fine. We'll make sure they cook through later. Remove the chicken to a plate.
While the chicken is searing, peel and dice the garlic cloves.
Once the chicken is out of the pan, reduce the heat to medium.
If there's still about 2 tablespoons of oil in the pan, great. If not, add more olive oil until you have about 2 tablespoons.
Add the garlic and red pepper flakes (if using) and stir frequently until the garlic is golden brown, about 1-2 minutes.
Pour in the coconut milk/lemon sauce and use a wooden or silicone spatula to scrape up all the yummy brown bits on the bottom of the pan. Not only does this add all the flavor to the sauce, it basically cleans the pan for you!
Once the sauce begins to simmer, return the chicken to the pan. Cook until the chicken reaches 165° in the thickest part of the breast, about 4-8 more minutes, depending on their size. (Some breasts might finish cooking before others; just remove each one as it's done.)
Remove the chicken to a serving platter.
Add the artichokes, olives, capers, reserved lemon zest and most of the chives to the sauce. Stir for 1 minute until warmed through. Taste and adjust seasoning if necessary.
Pour the sauce over the chicken and sprinkle with the remaining chives. Serve with rice, veggie rice or steamed potatoes.