Hard to tell with the blurry picture Patty. Parsley & fennel are host plants for most of the swallowtail varieties...the cats are usually black & yellow striped. Yours looks like black with a band of white, so I don't know.
When they first hatch the Black Swallowtwail caterpillars are only around 2mm long, and are black with a white band around their middle. Unfortunately, my pictures of first instar Black Swallowtails are not clear enough to make out all these details.