Preheat the oven to 200C/400F/Gas 6.
Using a sharp knife, cut a pocket lengthways into the thickest part of the breast. Stuff the pocket with the cheese and fresh thyme and season the breast with salt and freshly ground black pepper.
Heat the olive oil in an ovenproof frying pan over a medium heat and add the crushed garlic. Fry for one minute then add the chicken breast and fry until golden-brown. Turn the breast over and transfer to the oven to roast for 10-12 minutes, or until cooked through.
For the basil oil, place the olive oil and fresh basil leaves into a food processor and blend until smooth.
For the salsa, finely chop the avocado into small cubes and place into a bowl. Sprinkle over the chopped chilli and squeeze over the lime juice.
To serve, place the chicken onto a warmed plate. Add a spoonful of the salsa and drizzle the fresh basil oil around the edge of the plate.