Preheat the oven to 450 degrees. Rub the olive paste on both sides of each chicken breast half.
Cut the potatoes into 1/16th-inch slices and thinly slice the tomatoes. Set 4 12-inch squares of foil on the counter. Lightly oil the center of each piece of foil and spread some potato slices in the middle; season them with salt and pepper. Cover the potatoes with a chicken breast half, then cover with more potato slices, salt and pepper and the tomato slices. Wrap the chicken airtight, in a deli sandwich wrap, and set the packages on a baking sheet. Bake for 30 minutes.
When the chicken is done unwrap the packages carefully (be careful the steam which will escape when you open the packages does not burn your hands.) Transfer the chicken, potatoes, tomatoes and the natural juices to deep plates.
Variations: Instead of the potatoes spread 1/2 cup drained canned white beans, a couple of slivers of fresh garlic, a leaf or two of fresh sage and a teaspoon of extra virgin olive oil underneath the chicken. Top the chicken with the tomatoes. Or spread each chicken breast half with 1 teaspoon each of oriental sesame oil, soy sauce and rice vinegar. Top each chicken breast half with 1/2 cup sliced jicama; 1 cup raw fresh spinach and 1 sliced scallion. Open and garnish with sesame seeds. Or, instead of the green olive paste and tomatoes, season each chicken breast half with barbecue sauce or ketchup and top with 1/2 cup of frozen corn kernels; leave the potatoes in (especially good for kids)