sp_grantdbaccess cannot be run in a stored proc owned by DBO?
Ownership chaining works only inside the database. sp_grantdbaccess lives in master and is therefore excluded from ownership chaining. Even worse, according to the sp_grantdbaccess topic in SQL Server 2000's Books Online:


  Only members of the sysadmin fixed server role, the db_accessadmin and db_owner fixed database roles can execute sp_grantdbaccess.


Erland Sommarskog wrote a great article on ownership chaining; however, it covers SQL Server 2005 and later, and there were some significant changes in the security model, so proceed with care when reading.

The only way I can think of to make this work is a hack: Create a loopback linked server and elevate the permissions that way: https://stackoverflow.com/questions/982782/sql-server-2000-execute-as

But be aware that that opens a big security hole.

So my best recommendation - I know you probably don't want to hear this now - is to upgrade to a more modern version of SQL Server.