In a small glass bowl, whisk together 0.5 tablespoon of olive oil, lime juice, lime zest, minced garlic, sea salt, and black pepper to create the marinade.
Place the chicken breast in a shallow dish and pour half of the lime-mint marinade over it, turning to coat evenly, and let it marinate for 15 minutes.
Preheat a grill pan or cast-iron skillet over medium-high heat and lightly grease with a touch of oil.
Grill the chicken breast for approximately 6 to 7 minutes per side, or until the internal temperature reaches 165 degrees Fahrenheit and the edges are slightly charred.
While the chicken rests, combine the cooked quinoa, diced cucumber, and chopped fresh mint in a large mixing bowl.
Drizzle the remaining olive oil and the rest of the lime marinade over the quinoa mixture and toss thoroughly to combine.
Slice the grilled chicken into thin strips and arrange them over the cucumber and quinoa base, garnishing with extra mint leaves if desired.