The deployment slipped by three weeks — tell the customer's CTO

Open with the headline ("I'm calling because the milestone we committed to has slipped by three weeks, and I want to be the one to tell you before you hear it elsewhere"). State what was missed, in plain terms. State what changed (a regulatory blocker, a dependency on your team's integration spec that surfaced during data QA). State what you are doing about it now, with a hard new date and the assumptions. Then ask the CTO what is hardest from their side and what you can de-scope. Do not promise that you will "find a way" without a concrete plan; that loses trust.