Step 1Place 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 2Wash 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.