Thank you for your help. No, I'm not trying to access the cube remotely. This is a brand new SQL Server 2012 developer edition install with the default accounts on a laptop. The error occurred when I tried to process a dimension I created. I've done a lot of Google searches trying to get an answer and this article on the link below seemed to be the most relevant information:
By changing the MSSQLServerOLAPService service to run under a domain or local user account that is a member of the OLAP Administrators group on the OLAP server and that has privileges on SQL Server, OLAP Services will be able to successfully process.
My settings are: In my SQL Server Configuration Manager>SQL Server Analysis Services>Properties>Log On As>This account: NT Service\MSSQLServerOLAPService [with a default password supplied during the install]
I don't know if the accounts are correct or how to find the OLAP Administrators group on the OLAP server in a Windows 7 environment. I am very new to SSAS.