Arrange the cubed chicken in a medium bowl and toss with 1/2 cup olive oil, lime juice, jalapeno and cilantro. Season lightly with salt. Let marinate for about 1 hour, refrigerated.
In a skillet large enough to hold all of the chicken in 1 layer, heat the remaining 1 tablespoon oil. Saute the chicken just to brown on all sides.
Preheat the oven to 525 degrees F. Brush the rolled out pizza dough lightly with oil and top the pizza dough with the mozzarella, fontina, plum tomatoes, eggplant, onion, chives, Parmesan, and chicken. Place on the pizza stone and cook for 15 to 20 minutes, or until done.
In a small bowl, dissolve the yeast and honey in 1/4-cup warm water.
In a mixer fitted with a dough hook, combine the flour and the salt. Add the oil, yeast mixture, and the remaining 3/4 cup of water and mix on low speed until the dough comes cleanly away from the sides of the bowl and clusters around the dough hook, about 5 minutes. (The pizza dough can also be made in a food processor fitted with the steel blade. Pulse once or twice, add the remaining ingredients, and process until the dough begins to form a ball).
Turn the dough out onto a clean work surface and knead by hand 2 or 3 minutes longer. The dough should be smooth and firm. Cover the dough with a clean, damp towel and let it rise in a warm spot for about 30 minutes. (When ready, the dough will stretch as it is lightly pulled).
Divide the dough into 4 balls, about 6 ounces each. Work each ball by pulling down the sides and tucking under the bottom of the ball. Repeat 4 or 5 times. Then on a smooth, unfloured surface, roll the ball under the palm of your hand until the top of the dough is smooth and firm, about 1 minute. Cover the dough with a damp towel and let rest 15 to 20 minutes. At this point, the balls can be wrapped in plastic and refrigerated for up to 2 days.
To prepare each pizza, dip the ball of dough into flour, shake off the excess flour, place the dough on a clean, lightly floured surface, and start to stretch the dough. Press down on the center, spreading the dough into an 8-inch circle, with the outer border a little thicker than the inner circle. If you find this difficult to do, use a small rolling pin to roll out the dough.