Or, if you're a Creationist, the antediluvian period, about 6000 years ago.
But the Bible says all creatures two by two*. Didn't the dinos make the boat? If not, the all creatures part is wrong. But that would mean there is an error in the Bible. Therefore there had to be dinosaurs on the Ark, and the Dinosaurs are still around.
Now I'm confused.
(* OK, trivia detail, there were seven pairs of Kosher animals...)