Combine boiling water and sun-dried tomatoes in a bowl; let stand 30 minutes or until soft. Drain and chop.
Heat oil in a large nonstick skillet over medium-high heat. Add onion, oregano, and garlic; cook 3 minutes or until onion is tender, stirring occasionally. Add spinach; cook 3 minutes or until liquid almost evaporates. Add tomatoes; cook 1 minute. Place spinach mixture in a bowl; cool 5 minutes. Stir in cheeses, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
Slice each breast half lengthwise, cutting to, but not through, other side. Open halves, laying breast flat. Place each breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/4-inch thickness using a meat mallet or small heavy skillet. Sprinkle chicken with remaining 1/4 teaspoon salt and remaining 1/8 teaspoon pepper.
Divide spinach mixture into 4 equal portions; spoon each down center of each breast half, leaving a 1/2-inch border at each end. Fold breast sides over filling.
Place a 2-foot-long sheet of heavy-duty plastic wrap on a work surface with 1 long side hanging over the counter's edge by 2 inches. Place a stuffed breast half, seam side down, on the end farthest from you, and tightly roll the chicken toward you, jelly-roll fashion. Twist the ends in opposite directions to form a cylinder. Tie plastic wrap in tight knots against the chicken on each end. Trim off excess wrap close to the knots. Place a second 2-foot-long sheet of heavy-duty plastic wrap on the work surface; place rolled chicken on wrap, and repeat procedure. Repeat with remaining breast halves.
Bring 3 quarts water to a boil in a large stockpot; add chicken. Simmer 15 minutes (do not boil), turning occasionally. Remove from water, and let stand 10 minutes before unwrapping and cutting into 1/2-inch-thick slices.
Wine note: In matching this dish with wine, the tomatoes, spinach, garlic, and cheeses are more important factors than the mild-flavored chicken. A terrific match for this savory lineup is the famous Italian light red wine Chianti Classico, especially riservas. Great producers include Querciabella, Ruffino, and Antinori. -Karen MacNeil