It actually seems like a somewhat likely scenario:
http://walterfootball.com/draft2013.php
Kansas City Chiefs: Tyler Wilson, QB, Arkansas 
It's pretty evident that the Chiefs will need to admit they were wrong and move on from Matt Cassel. I'm sorry, Eric Winston, but he's just too limited to command a winning team in today's pass-happy NFL, and he's become a turnover machine in the wake of Charlie Weis' departure. The fans obviously know it too based on the reaction they supposedly had when he suffered a concussion.
Kansas City has to take a quarterback; in fact, the front office may have to trade up to acquire one.