Preheat broiler. Place an oven-safe rack approximately 4 inches from heat. In a large bowl toss bread cubes with olive oil, oregano and salt. Arrange on a baking sheet in an even layer.
Toast under broiler for 3-5 minutes, turning once half way through. Set aside and let them cool. Store in a plastic bag if you made ahead of time.
Dressing:
In a small bowl combine red wine vinegar, mustard, garlic, brown sugar and salt. Whisk continuously. While whisking pour oil in a steady stream. Whisk until well combined. Set aside.
For Chicken:
Heat a skillet over medium-high heat. Season chicken breasts with salt and pepper. Brown on both sides, cooking about 5 minutes on each side or until throughly cooked. Place on a cutting board. Wait 3-5 minutes. Cut into slices.
For Salad:
Arrange lettuces, cucumber, grape tomatoes and red onion on salad plates. Top with bread cubes and chicken. Drizzle with the desired amount of dressing.