Boil a large pan of water, add the rice, and simmer for 15 minutes until the rice is tender. Pour into a sieve and leave to drain.
While the rice is cooking, heat a cast iron griddle pan on high heat and brush on a little oil.
Sprinkle the Cajun seasoning and pour half the oil on the chicken breasts, rubbing it in using your hands. Flatten the chicken breasts slightly with your hands and place on the hot griddle. Cook for 7-10 minutes, turning once, until the chicken is charred and no longer pink in the middle. Place on a chopping board to rest while you cook the vegetables.
Brush the rest of the oil on the griddle and place the peppers and onion on in a single layer. Cook for 5-6 minutes, turning a couple of times, until lightly charred.
By now the rice should be cooked and drained. Fluff it up with a fork and stir through the coriander and lime zest.
Divide the rice between two bowls. Cut the chicken breasts into slices and place on top of the rice. Add the char-grilled peppers and onion and top with the chopped avocado.