Pat the chicken breast dry with paper towels and season both sides evenly with the sea salt, black pepper, garlic powder, and dried oregano.
Preheat a grill or a cast-iron grill pan over medium-high heat and lightly grease with a small amount of oil to prevent sticking.
Place the chicken on the grill and cook for 6 to 8 minutes per side, or until the internal temperature reaches 165 degrees Fahrenheit and the meat is no longer pink.
Transfer the chicken to a clean plate and let it rest for 5 minutes to ensure the juices redistribute for maximum tenderness.
While the chicken rests, halve the cherry tomatoes, dice the cucumber, and thinly slice the red onion.
In a small mixing bowl or mason jar, whisk together the extra virgin olive oil and fresh lime juice until the dressing is well combined.
In a large salad bowl, combine the mixed greens, tomatoes, cucumber, and red onion, then drizzle with the lime vinaigrette and toss to coat.
Slice the grilled chicken into thin strips and arrange them over the salad, then top with the fresh avocado slices and serve immediately.