Prithee (Interjection): used to express a wish or request

From “Young Goodman Brown” by Nathaniel Hawthorne.
“Ha! ha! ha!” shouted he, again and again; then composing himself, “Well, go on, Goodman Brown, go on; but prithee, don’t kill me with laughing!”  (Paragraph 24)

I now understand that he was being “requested” not to continue making comments that were humorous, by the response of “Don’t kill me with laughing!”.