Step 1 Place the chicken breasts in a Dutch oven or large skillet. Add water to just cover, about 3 cups, and salt to taste. Bring to a boil over medium-high heat, reduce the heat to low and simmer, covered, 15 minutes. Drain, reserving the broth. Combine the almonds and 1/2 cup of broth in a blender and blend until the nuts are very finely chopped but not pureed. Set aside.
Step 2 Wash out the Dutch oven or skillet and wipe it dry. Add the oil and heat over medium heat. Add the onion and garlic and cook until tender, about 5 to 7 minutes. Meanwhile, puree the tomatoes in the blender. Add the tomatoes and ground almonds to the onion mixture. Add 1/2 teaspoon of salt or more to taste and a few grinds of pepper. Bring to a boil, reduce the heat and simmer, uncovered, 15 minutes. If the sauce becomes too thick, thin with a little broth.
Step 3The chicken and sauce can be prepared in advance to this point and refrigerated until needed. Slice the chicken breasts lengthwise. Reheat the sauce in a large skillet. Add the sliced chicken to the skillet and cook until heated through, 10 to 15 minutes.