Heat the olive oil on medium high in a large skillet. Brown the chicken on all sides. During the last minute of browning, add the garlic to the pan, between the chicken pieces, and cook just until soft.
Pour in the tomatoes and artichokes including their juices. Stir in the sugar. Bring to a boil. Lower the heat and simmer uncovered, turning the chicken pieces occasionally to cook evenly. Chicken will take approximately 20 minutes to cook through.
Turn the chicken pieces so that the top faces up. Crumble the feta on top and heat just until feta starts to melt.
Garnish with generous handfuls of the fresh herbs.
Note: The pan will have lots of juice with flecks of feta chunks. Spoon the chicken and sauce into a shallow bowl over cooked orzo or other pasta.