Combine the olive oil, lemon juice, garlic, oregano, salt, and pepper. Coat the chicken and refrigerate for 20 minutes.
Whisk the olive oil, lemon juice, Dijon, honey, parsley, salt, and pepper until blended. Set aside.
Preheat the grill or grill pan to medium-high. Grill the chicken for 5 to 7 minutes per side, depending on thickness, until the center reaches 165°F (74°C). Rest for 5 minutes before slicing.
Grill the zucchini slices for 2 to 3 minutes per side until tender with visible grill marks. Chop into bite-size pieces.
Divide the quinoa and arugula among four bowls. Add the zucchini, corn, tomatoes, cucumber, avocado, and sliced chicken.
Spoon the lemon vinaigrette over each bowl and serve immediately with extra lemon if desired.