Hi Sandyjay - glad to see you made it to the forums - welcome!
What you have there is a swallowtail butterfly - the caterpillars feed on dill, fennel, parsley, carrot, rue (lots of things in the carrot family).
Check out these images for help in identifying the type of swallowtail:
If you still can't ID it please feel free to email the images to me.
Hope this helps!