I don't know why this is even up for discussion. Not only is the Chronoverse real, but I'm Crono's dad. That's right bitches, I'm Crono's old man! I don't know how exactly that came to happen, but it's probably quantum. Here's how it went down:
Forget about the Chronoverse for a minute. Somewhere else out there is a dimension where I'm Emperor of the Universe. In that dimension I am the shit, and I also happen to be married to all the hottest actresses in Hollywood--42 million in all--each of whom also happens to be a super-genius thanks to some accidental IQ-boosting shampoo invented by Will Wright in 1989. One day this hawesome Josh told them this:
"Legion of gorgeous genius wives: I need you to invent a transdimensional teleporter. You see, my scientists have speculated that, despite it being beyond all belief, there are other dimensions out there. And in every single one of these dimensions, I'm actually hella lame. So here is what I propose: The first person to invent the teleporter gets to stay with me, and all the rest of you get shipped off to these other Joshes, one apiece. Kapeesh?"
Needless to say, I got 61,999,999 million fully operational transdimensional teleporters delivered to me simultaneously. So I let 'em all stay! The only woman who didn't invent a teleporter had actually been out sick that day, so instead of shipping her off to a needy Josh somewhere, I let her off easy: I told her that she would still have to go pair off with a needy Josh somewhere, but that, in so doing, she would get to create a spiky-haired kid so friggin' hawesome that his adventures would be the subject of famous video games in practically every single dimension. So I shipped her off to the Chronoverse, which, as you might expect, had been called up to that point the "Identitycrisisverse." She and the Josh there got it off, and then there was Crono.
Ah, but that's not the end of the story, you unfathomable fools! You see, the Josh in that universe also speculated as to the existence of other dimensions, and came up with the idea that, somewhere, there was a dimension that he would suddenly be sucked into. And, lo and behold, he was! That was me, and this universe is that universe!
IT ALL MAKES PERFECT SENSE!!