1. Prepare grill to medium-high heat.
2. To prepare jam, heat a large nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion; sauté 5 minutes. Reduce heat to medium-low; stir in sugar, vinegar, and thyme. Cover and cook 10 minutes or until onion is very tender. Remove from heat.
3. To prepare burgers, combine oregano, salt, garlic powder, and beef. Divide mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty. Place on grill rack coated with cooking spray; cook 2 minutes. Turn patties over. Place 1 cheese slice on each patty; cook 2 minutes or until done.
4. Spread cut sides of each bun with 1/2 teaspoon mayonnaise. Place 1 patty on bottom half of each bun; top each with 1/4 cup onion jam and bun top.
Baked chips and blue cheese dip: Combine 1/2 cup (2 ounces) low-fat crumbled blue cheese, 1/3 cup reduced-fat sour cream, 2 tablespoons canola mayonnaise, and 1 teaspoon red wine vinegar in a bowl. Mash with a fork.