If using wooden skewers, soak them in water for at least 30 minutes so they don’t burn on the grill.
Make the marinade: In a large bowl (or zip-top bag), whisk together olive oil, lemon juice, minced garlic, oregano, paprika, salt, and black pepper.
Add chicken cubes and toss to coat well. Marinate for at least 15 minutes, or up to 2 hours in the refrigerator for deeper flavor.
Thread chicken and cherry tomatoes onto skewers, alternating pieces. Leave small gaps between pieces so heat can circulate.
Preheat grill to medium-high heat (about 400°F / 205°C). Clean and lightly oil the grates.
Grill skewers for 10–12 minutes total, turning every 2–3 minutes, until lightly charred and the chicken reaches 165°F (74°C) in the thickest piece.
Transfer skewers to a plate and rest 3–5 minutes before serving. Serve warm (optional: finish with an extra squeeze of lemon).