To add the primary client to a deal, click the "People" tab on the deal and click the "Relate a contact" button.  

To select an existing contact in your database, type a portion of their name then choose your contact from the picklist.  

After you have selected the contact, then select "Primary client" from the "Relationship" box. Note that it is the last entry on the list.
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Here's a quick article about this.