1. Saute the chicken breasts in the olive oil in a large pot over medium/high heat. Cook the chicken on both side until done -- about 7-10 minutes per side. Cool the chicken until it can be handled. Do not rinse the pot.
2. Shred the chicken by hand into bite-sizes pieces and place the pieces back into the pot.
3. Add the remaining ingredients to the pot and turn heat to high. Bring mixture to a boil, then reduce heat and simmer for 4-5 hours. Stir mixture often so that many of the chicken pieces shred into much smaller bits. Chili should reduce substantially to thicken and darken (less orange, more brown) when done.
4. Combine some chopped Italian parsley with sour cream and serve it on the side for topping the chili, if desired.