Can't add event to Google Calendar

When I try to add an event I get a popup window like this:

"Before you can add an event, you must add at least one Calendar account to the device and make a calendar visible. Touch 'Add account' to add an account (if you just added an account, wait for it to finish syncing and try again). Or touch Cancel and ensure that at least one calendar is visible"

I have a Google Calendar and it works fine on the web. If I try to add the account, it says that it already exists.

Any ideas?