10 oil-packed anchovy fillets, finely chopped
4 garlic cloves, finely grated
1 1/2 cups green olives (such as Castelvetrano), plus 1/2 cup brine reserved
1/2 cup olive oil
1 tablespoon finely grated lemon zest
2 tablespoons fresh lemon juice
Kosher salt, freshly ground pepper
1 small onion, thinly sliced
1/2 cup coarsely chopped fresh oregano, plus leaves for serving
1 (3 1/2–4-pounds) chicken, halved lengthwise
Vegetable oil (for grilling)
Tomatoes in Chile-Fennel Oil
Toss anchovies, garlic, olive brine, olive oil, and lemon juice in a medium bowl; season with salt and pepper. Place half of anchovy mixture in a large resealable plastic bag; add onion and chopped oregano. Cover and chill remaining anchovy mixture.
Season chicken with salt and pepper and add to bag, seal bag, and toss to coat. Let marinate 4–12 hours.
Prepare grill for medium heat; generously oil grate with vegetable oil. Remove chicken from marinade, letting excess drip back into bag (a few pieces of onion and oregano still clinging are okay); discard marinade. Starting skin side up, grill chicken, turning occasionally, until lightly charred and cooked through, 30–40 minutes.
Meanwhile, set out reserved anchovy mixture and let come to room temperature. Use the side of a chef's knife to smash olives, crushing and pitting them at the same time (smash again if very large). Add olives and lemon zest to anchovy mixture.
Place chicken on top of Tomatoes in Chile-Fennel Oil and spoon anchovy-olive mixture around. Top with oregano leaves.
Chicken can be grilled 4 hours ahead. Store at room temperature and assemble dish just before serving.