Prepare a grill for medium heat.
Put the grated garlic into a large resealable bag. Add 1/4 cup oil, the lemon zest and juice, oregano and the chicken. Seal the bag tightly and use your hands to vigorously massage the marinade into the chicken, making sure that the chicken is evenly coated. Marinate for at least 10 minutes at room temperature.
Meanwhile, remove the rind from the watermelon, cut the fruit into 1-inch cubes and put in a large mixing bowl. (You should have about 6 cups total.) Quarter the cucumber lengthwise and cut into 1-inch pieces. Place on top of the watermelon in the mixing bowl. Cut the feta into 1/2-inch cubes, put on top of the cucumber and top with the Kalamata olives. (Do not mix yet.) Reserve.
Remove the chicken from the marinade and place on a platter. Lightly oil the grill grates. Sprinkle the chicken liberally with salt and pepper and arrange the pieces skin-side down on the grill, leaving some space between the pieces. Cook until the skin is lightly charred and releases itself from the grill, about 2 minutes. Then rotate the chicken about 90 degrees so that the skin won't burn and cook another 2 minutes. Flip and cook for an additional 5 minutes. Cover the grill and cook until an instant-read thermometer inserted into the deepest part of each chicken thigh reads 165 degrees F, about 5 more minutes. Transfer to a platter and rest for at least 5 minutes before serving.
While the chicken is resting, brush the cut sides of the baguette halves with 2 tablespoons oil and sprinkle with salt and pepper. Arrange the bread cut-side down on the grill until lightly charred and warmed through, about 2 minutes. Halve the remaining garlic clove and lightly rub the cut sides of the garlic onto the hot bread. Halve each piece of baguette.
Scatter most of the mint over the watermelon mixture. Add the remaining 1/4 cup extra-virgin olive oil and a large pinch of salt and pepper and gently stir to combine.
Divide the watermelon salad among 4 large dinner plates along with a piece of chicken and some bread. Garnish with the remaining mint and serve immediately.
If using a charcoal grill, be sure to allow a little extra time to let the coals reach the proper temperature.
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