You may have gotten a borked file in the download. It's working fine for me.
May need to use the repair tool on the patcher.
May need to entirely redownload the LoL client.
Both of those take stupid amounts of times, so try just restarting your computer and trying again first. If that doesn't work, send a support ticket just to make sure you don't have to, though they'll likely ask if you used the repair tool or not.