You would need 1 CAL, not 3 CALs for that user. The CRM 2013 User CAL is good for all CRM 2013 servers deployed within your organization.
So if your 100 employee organization deployed 4 CRM servers with 2 organizations and gave all employees access to both organizations you would need 4 server licenses and 100 User CALs.
See page 7 of this PDF: https://partner.microsoft.com/download/global/40196599