Stem and coarsely chop oregano. Add half the oregano (reserve remaining for dressing and garnish) to a medium mixing bowl and mix with 2 tsp. olive oil, 1/4 tsp. salt, and a pinch of pepper. Rinse chicken breasts and pat dry. Add chicken to bowl and toss to coat. Marinate at least 10 minutes. While chicken marinates, prepare ingredients.

Trim cucumber, halve lengthwise, and cut on an angle into 1/4” half-moons. Hold romaine head at root end and chop coarsely. Rinse olives and halve lengthwise. Halve Roma tomato lengthwise and slice halves into 1/4" half-moons.

In another medium mixing bowl, combine half the feta (reserve remaining to top salad) and sherry vinegar. Crush feta into a coarse mash. Whisk in remaining oregano (reserve a pinch for garnish) and 2 Tbsp. olive oil and season with a pinch of salt and pepper.

Heat 1 tsp. olive oil in a medium non-stick pan over medium heat. Add chicken to hot pan and cook until browned and chicken reaches a minimum internal temperature of 165 degrees, 5-6 minutes per side. Wash marinade bowl with hot soapy water. Transfer cooked chicken to clean bowl, rest 5 minutes, and shred into bite-size pieces with two forks or your hands. Toss pieces with 2 tsp. dressing (reserve remaining for salad).

Add cucumbers, romaine, olives, tomato, remaining dressing, and remaining feta to bowl with chicken and toss to coat. Taste, and season with a pinch of salt and pepper if desired.

Serve salad on a plate and garnish with remaining oregano.