Place the smoked paprika, garlic, cumin, caraway seeds, chipotle pepper, and adobo sauce into a mortar, and grind together with a pestle to make a paste. Smear the paste all over the chicken breasts, place into a bowl, cover, and refrigerate at least 4 hours or overnight.
Preheat an outdoor grill for medium heat, and lightly oil the grate.
Remove chicken from marinade, and discard the excess marinade. Brush the chicken breasts with olive oil, and sprinkle with salt and pepper. Grill the chicken breasts until the meat shows grill marks and the inside is no longer pink, about 5 minutes per side.
