4 garlic cloves, finely grated

2 Tbsp. dried oregano

1 tsp. sugar

⅓ cup plus 1 Tbsp. extra-virgin olive oil, divided; plus more for drizzling

1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, plus more

Freshly ground pepper

1½ lb. skinless, boneless chicken thighs, cut into 2″ pieces

1 15.5-oz. can chickpeas, rinsed

2 tsp. ground cumin

2 tsp. smoked paprika

3 Tbsp. fresh lemon juice, plus more for drizzling

½ small red onion, thinly sliced

1 lb. mixed tomatoes, cut into bite-size pieces

½ cup pitted Kalamata olives

6 oz. feta, thinly sliced

Parsley leaves with tender stems, pitas, and lemon wedges (for serving)

Eight 10″-long bamboo skewers, soaked 30 minutes in water, or metal skewers