In a medium bowl, mix together the garlic powder, paprika, 1 teaspoon of salt, and a few grinds of black pepper. Add the chicken and toss to coat well. This can be done a day in advance, if desired.
Make the pesto, if making from scratch. See recipe below. Blend ⅔ cups of pesto with 2 cups of water or stock until combined. Set aside.
In a 10-inch straight-sided saute pan, warm the oil over medium heat. Add the chicken pieces in one layer and brown on two sides, about 2-3 minutes each side. Do not cook through and do not brown too much. Transfer the chicken back to the bowl (it doesn’t matter that this had raw chicken in it since the chicken still has to be cooked again.)
Add the onion to the pan and sauté until slightly tender, about 5 minutes. Add the garlic and 1 teaspoon salt (be conservative if using a seasoned stock) and cook until fragrant, about 1 minute.
Add the tomatoes to the pan and raise the heat, scraping the bottom of the pan to deglaze and remove the bits stuck to the bottom. (If using cherry tomatoes, add with the next ingredients.)
Add the rice, pesto water/stock, olives, and artichoke hearts and bring the liquid up to a boil. Arrange the chicken pieces on top. Lower the heat to a simmer, cover and cook for 20 minutes. Most of the liquid should have been absorbed. Test the rice for tenderness. If the water has been absorbed, but the rice is not perfectly done, keep it covered and off the heat for another 10 minutes.
Garnish with herbs (if using) and serve immediately or allow the dish to sit off the heat, covered, for up to 20 minutes. Drizzle with extra pesto and fresh basil, if desired, and mix everything together before serving.