Cook Jasmine rice: Mix 1/2cup of rice with 3/4 cup of water, salt and butter. Bring to boil, cover and cook for 10 minute Remove from heat and let sit for 5 minute Fluff before serving.
Salsa: Halve the avocado lengthwise. Slice one half (save for garnish) and roughly chop the other half. Core the plum tomatoes, and roughly chop. Slice and chop the onion into similar sized pieces. Mix all in a bowl. Cut 2 wedges out of lime and juice the rest. Add the lime juice to the bowl and season to taste with salt and pepper. Set aside.
Stir 1 teaspoon salt, 1/4 teaspoon black pepper, and cayenne pepper together in a small bowl. Rub evenly into the chicken breasts.
Heat the olive oil in a skillet over medium heat; cook the chicken in the heated oil until no longer pink in the center and the juices run clear, 5 to 7 minutes per side.
To Plate: Place chicken on top of 1/2 cup rice. Top with avocado salsa. Place sliced avocado and lime wedges for garnish.