Make a marinade with the garlic, onion and lime juice.
Arrange the chicken pieces in a shallow glass baking pan. Pour the marinade over the chicken pieces and mix them up so that all of the pieces are well coated. Cover with plastic wrap and refrigerate for about 2 to 3 hours.
After marinating, season the chicken pieces on the top layer by eye with salt, pepper, cumin, and oregano.
Heat vegetable oil in a large skillet, deep enough to cover half the thickness of the chicken at one time.
Mix the flour with the salt and pepper and place in a shallow pan. Make an egg wash by beating a whole egg with a little water.
Remove the chicken pieces from the marinade (shaking off some of the excess marinade), dip each piece in the egg wash, and dredge in the seasoned flour mixture. (As you work down a layer, re-season the newly exposed layer with more salt, pepper, oregano, and cumin.)
Fry the chicken pieces in small batches (don't crowd the pan), until all sides are golden brown and the chicken is completely cooked through.
Serve with cooked white rice.