1. Preheat oven to 400°.
2. Place mushroom caps, gill sides up, on a rimmed baking sheet; drizzle with oil and vinegar, and season with salt and 1/4 teaspoon pepper. Bake until caps are just tender, about 10 minutes.
3. Meanwhile, combine tomato, olives, breadcrumbs, cheese, and chives in a medium bowl. Season with remaining 1/4 teaspoon pepper.
4. Divide tomato mixture evenly (about 1/2 cup per mushroom) among portobello caps. Bake 10-12 minutes or until lightly browned and mushrooms are tender. Serve hot.