Preheat oven to 375°. Heat oil in a large dutch oven over medium-high heat. Sprinkle chicken all over with salt and lay in hot oil, skin side down. Cook until browned, about 5 minutes. Turn chicken over and add 1 cup water, the garlic, and artichokes.
Roast chicken in oven, uncovered, until cooked through, about 1 hour. Add olives and parsley.
Prep hearts: Snap off thick green outer leaves down to yellowish core. Halve artichokes crosswise; discard thorny tips. Trim stem to about 1/2 in. and peel tough outer skin from remaining stem. Halve artichoke lengthwise; scoop out and discard fuzzy, red-tipped choke. Put hearts in cold water with a little lemon juice and set aside until you're ready to cook.
Note: Nutritional analysis is per serving.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.