Heat oil in a large skillet with a lid over medium heat. Brown chicken breasts 4 minutes on each side, sprinkling the salt evenly over them as they cook.
Remove chicken from pan and set aside.
Add all remaining ingredients to the pan (tomatoes, raisins, lemon juice, brown sugar, ginger, cinnamon, pepper, cardamom).
Bring sauce to a boil, then reduce heat and simmer 3 minutes.
Add chicken back to the pan. Spoon some of the sauce over the chicken.
COVER and simmer 8 minutes.
Flip the chicken over, spoon sauce on top, then cook for an additional 5-8 minutes until chicken is cooked through (165 F on meat thermometer).
Remove chicken from pan and set aside for 10 minutes to let cool.
MEANWHILE, keep simmering the sauce, uncovered, until it reduces and thickens to your preferred consistency.
Slice the rested chicken then serve hot atop couscous or rice. Pour the raisin sauce over the chicken.