I recently went to fix 2 Macs that had been updated to Mavericks and were displaying login prompts below for Keychain Access

• CalendarAgent
• accountsd
• AddressBookSourceSync

There are multiple fixes on the internet which eventually fixed them both

First Fix

• Open Up Keychain Access
• Click on Preferences
• Go to General
• Reset My Default KeyChain
• Go back to Preferences then choose KeyChain First aid and run a repair and fix

Second Fix

• In Finder Select Go in Top Toolbar while pressing the Option key and Click on Libray
• Go into the /Keychains/ Folder
• Look for a folder with a name similar to this “A8F5E7B8-CEC1-4479-A7DF-F23CB076C8B8”.
• Move this folder to the Trash.
• Immediately choose Apple Menu (?) > Restart… to restart your Mac.

Third Fix

• Go into Keychain
• Choose Preferences
• Choose First Aid Tab
• Choose “Syncronise login keychain password with account”

Try this if it’s asking you every 5 minutes, instead if just on startup.

http://www.igorkromin.net/index.php/2013/10/28/calendaragent-wants-to-use-your-login-keychain-messages-after-upgrading-to-os-x-mavericks/