Can a 1/4" Chisel cut a 1/4" mortise?

Okay, let me be honest. I'm not really a Neanderthal, though I want to be.

I am trying to cut mortises by using a router and squaring the result with a chisel. But my 1/4" Lee Valley chisel doesn't fit the hole. To be more specific, it does at the tip of the chisel, but about 1" up the chisel blade, it gets wider by just over 1/64" of an inch, so it doesn't easily go to the bottom of the mortise.

Is this normal for a 1/4" chisel, or should I get a new one?

Thanks for any help. I posted here because I thought hand tool experts whould know better about chisels.

--Dave