Found the answer on a Google Groups forum:
• Launch /Applications/Utilities/Keychain Access
• Select "System" from the Keychains menu in the upper left
• Select "Certificates" from the Category menu in the lower left
• Find the entry that corelates to your computer's name in the list on the right, and click on the disclosure triangle.
• Secondary click on the "Private Key" entry that appears and select "Get Info" from the contextual menu that appears.
• Select the Access Control tab.
• You can then either add AnyConnect to the the list at the bottom of the screen (more secure, but you will need to repeat this process anytime the version of AnyConnect changes), or toggle the radio button to "Allow all applications to access this item".
A similar answer shows a picture but provides fewer instructions