In the run-up to the June 30 deadline for a comprehensive nuclear agreement with Iran, alarmists in Washington, Tel Aviv and elsewhere are again warning of an imminent race to nuclear weapons capabilities in the Middle East—one that will occur in the guise of peaceful nuclear programs, as countries such as Saudi Arabia, Egypt and Turkey all rush to construct their first nuclear power plants.

But the logic of chain-reaction proliferation in the Middle East is critically flawed. Equally flawed are assumptions that the region’s nuclear power aspirants are anywhere near having operational programs. Ambitious rhetoric aside, including Saudi Arabia’s pledge to compete with Iranian enrichment levels, few countries in the region have meaningfully increased their civil or military nuclear capabilities in recent years. With the Gulf Cooperation Council summit at Camp David Thursday putting talk of a nuclear Middle East back into the headlines, it’s time for a reality check on the region’s actual capacity for both nuclear energy and nuclear weapons. ...