Why does Dropbox require Mac Keychain access?
Keychain is a password management system for Apple's Mac OS. Dropbox requires access to your Keychain to help verify your account and to provide another layer of security over your Dropbox application settings.
To grant Keychain access to Dropbox, simply click Allow or Always Allow (recommended for seamless access) when prompted to do so from Mac OS X.
Clicking Deny will result in a "Couldn't start Dropbox" error message. For security reasons, Dropbox will not start without access to your Keychain.
For more information about Mac OS X Keychains, consult Apple's Support Center.