It's a semantic paradox. Vidiot is right of course that 'eggs' existed many millions of years before the appearance of chickens, but if we word it more specifically: What came first the chicken or the chicken egg?
Now we have a genuine semantic paradox that dates back to ancient Greece and has had philosophers spilling way too much ink, but that's what philosophers do.
Scientifically speaking modern chickens are hybridized and domesticated descendants of Asian jungle fowl. Chickens were domesticated about 8000 years ago. Red junglefowl - Wikipedia