Season the chicken breast with 0.125 tsp sea salt, 0.125 tsp black pepper, and 0.25 tsp dried oregano.
Heat a grill pan or heavy skillet over medium-high heat and cook the chicken for 6 minutes per side until the internal temperature reaches 165°F.
While the chicken is cooking, whisk together the extra virgin olive oil, lemon juice, dijon mustard, and the remaining salt, pepper, and oregano in a small bowl.
Slice the cucumber into thin half-moons, halve the cherry tomatoes, and slice the avocado into thin wedges.
Allow the cooked chicken to rest for 5 minutes on a cutting board before slicing it into thin strips against the grain.
In a large bowl, toss the mixed baby greens with half of the prepared dressing, then top with the chicken, cucumber, tomatoes, and avocado before drizzling with the remaining dressing.