Whisk together the olive oil, lemon juice, cumin, paprika, cayenne, and thyme. Add a pinch of salt and pepper. Place along with chicken breast in a medium bowl or in a ziplock bag, seal. Marinate at room temperature for 30 minutes to 1 hour or in the fridge overnight.
Heat the grill. Add the chicken and cook until the chicken is no longer pink. Remove from grill.
In a medium bowl, whisk together the red wine vinegar and olive oil, along with a small pinch of salt and pepper. Add the vegetable toppings and combine.