Season the chicken breast evenly with half of the sea salt, half of the black pepper, and all of the dried oregano.
Heat a grill or grill pan over medium-high heat and cook the chicken for 6 to 7 minutes per side until the internal temperature reaches 165°F.
While the chicken is grilling, chop the romaine lettuce, cucumber, red bell pepper, and red onion into bite-sized pieces.
In a small glass jar or bowl, whisk together the extra virgin olive oil, lemon juice, Dijon mustard, and the remaining salt and pepper to create the dressing.
Remove the chicken from the heat and let it rest for 3 minutes before slicing it into thin strips.
Place the chopped lettuce, cucumber, bell pepper, onion, and shredded carrots in a large bowl and toss thoroughly with the lemon-dijon dressing.
Transfer the salad to a plate and top with the warm sliced chicken and the fresh avocado slices.