Pour the olive oil into a sauce pan. Heat on low (simmer), then add the onions and garlic, peppercorns and bay leaves.
Cook on simmer ( you don't want the onions or garlic to brown at all, just soften). This should take 5-7 minutes.
Add the vinegar and shredded chicken. Turn the heat off and stir the whole mixture to combine. Add salt to taste.
Pour the mixture into a glass container, then cover and allow to marinate for at least 2 hours, or up to overnight.
Serve cold or at room temperature with buttery crackers (like Ritz) or saltines.
Need to shred a ton of chicken? I use my handy Kitchenaid stand mixer to do it in about 30 seconds! Just toss the hot cooked chicken breasts into the mixing bowl. Make sure the beater attachment is in place. Raise the bowl and hit a low power setting for about 30 seconds. Voila, shredded chicken, in no time flat!