In a small saucepan, simmer balsamic vinegar and honey over medium heat until reduced by half. Set aside.
Season chicken breasts with salt and black pepper. Heat olive oil in a large skillet over medium-high heat. Cook chicken until golden on both sides and cooked through, about 6-8 minutes per side. Remove from the skillet.
Sauté minced garlic over medium heat until fragrant, about 1 minute. Add the cherry tomatoes and dried oregano. Cook for 3-4 minutes, stirring occasionally, until the tomatoes start to soften.
Return the sliced chicken to the skillet, nestling it among the tomato mixture. Top with mozzarella pearls. Cover and cook until the mozzarella is just melted, about 2-3 minutes.
Sprinkle fresh basil over the skillet and drizzle the balsamic glaze. Serve immediately.