Rinse the rice through a mesh strainer until the water runs clear. Place in a 3-quart or larger saucepan along with the saffron, salt, and vegetable broth. Set the heat to medium and let cook until the water has reduced beneath the level of the rice. Cover, turn the heat down to low, and simmer for 15 minutes. Turn off the heat and let sit until ready to serve.
While the rice cooks, slice the two chicken breasts in half length-wise to produce four thin breast pieces. Season both sides of each piece with the smoked paprika and pepper.
Heat the olive oil in a 12" or larger skillet over medium-high heat. Once hot, add the sliced onion and saute for 3 minutes. Push the onion to one side of the pan and add the chicken pieces. Immediately turn the heat down to medium. Let the chicken cook for 2 minutes, then turn the chicken and add the garlic, olives, prosciutto, capers, and tomatoes.
Allow the contents to come to a boil, then turn the heat to low and cover the pan. Simmer for 6 minutes, or until chicken is cooked through. Remove the cooked chicken from the pan and turn the heat back up to medium-high. Cook the sauce for 3 minutes to thicken. Serve the chicken topped with sauce and a side of saffron rice.