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First make the dressing: Combine the red wine vinegar with the sugar, olive oil, minced sweet onion, mustard and salt and white pepper in a blender and process until smooth.
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Refrigerate in a covered container until ready to use.
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Light a grill or charcoal barbeque and grill the chicken breasts until cooked through. You can also cook the chicken in your oven broiler - line the broiler pan with foil first.
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Set the cooked chicken aside, and when it is cool enough to handle, cut them into slices.
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Divide the lettuce on four chilled plates. Top with the grilled chicken slices, then the sliced strawberries and the pecan pieces. Drizzle some of the red wine vinaigrette over the top and serve.
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Save any extra dressing for another use.