The aioli is the star of this dish especially if you love garlic like I do. It's also fabulous on burgers and if your in a pinch you can use a store bought mayo, just add a little red wine vinegar, dijon, and olive oil to taste along with your garlic, but I strongly suggest you just make it from scratch because it will blow your mind!
Start with the aioli it can be made up to three days in advance. Preheat ove to 300. Slice off top of garlic, cutting through the cloves. Place cut side up in a pie plate or small baking dish, Drizzle with olive oil and sprinkle with salt and pepper. Roast until completely soft, 1 hour. Cool completely. Squeeze out cloves from papery skins and mash until smooth.
For aioli make sure all your ingredients are at room temp. Set a deep bowl on a damp dish cloth to prevent it from slipping as you whisk. Whisk egg yolks, dijon, vinegar, salt, and pepper together until thick and creamy.
Combine the oils in a measuring cup. Whisk the oil into the eggs a drop at a time until it begins to thicken. Add remaining oil in a thin steady stream until thick and glossy. Add roasted garlic. Taste, and adjust seasoning adding more vinegar, dijon, salt, or pepper to taste. Store in the refrigerator for up to three days.
Slice chicken breast through the middle horizontally to cut in half. Toss chicken, lemon, garlic, oregano, oil, and pepper togther. Cover and refrigerate for 20 minutes or up to overnight. Sprinkle with salt to taste. Grill over medium hot coals until opaque, with no trace of pink, 3-5 minutes per side. For indoor cooking preheat broiler, broil chicken until opaque, 3-5 minutes per side. Cut each loaf of baguette into 4 equal-sized pieces. Split and toast on grill until just crisp, 1 minute. Fill baguette with tomatoes, salad greens, chicken, and aioli. Serve warm.