1. Sprinkle chicken breasts with poultry seasoning. Grill in hot oven or in a George Foreman grill until juice runs clear and meat is white all the way through. Chill.
2. Place eggs is medium sized bowl. Add vinegar, pepper, salt, and mustard. Whisk briskly.
3. Continue to whisk, and slowly drizzle in oil until mayo is made and thickened. Place mayo in fridge. Directions go two ways from here, depending on what you want to use this chicken salad for.
4. For just eating, on lettuce, or with a spoon, finely chop shallots, including green parts, excluding roots. Coarse chop chicken breasts and mix with chopped shallots. Add mayo to taste.