This is according to The New York Times:
The commander in chief can also order the first use of nuclear weapons even if the United States is not under nuclear attack....
“There’s no veto once the president has ordered a strike,” said Franklin C. Miller, a nuclear specialist who held White House and Defense Department posts for 31 years before leaving government service in 2005. “The president and only the president has the authority to order the use of nuclear weapons.”
Some scholars (and Wikipedia entries) insist that a system of checks and balances puts the secretary of defense in the decision loop. But Bruce G. Blair, a research scholar at Princeton University who as an Air Force officer would have launched a nuclear missile if an order had come from the president, said that rule applied in the silos but not at the top of the command chain.
“There’s nothing the secretary of defense can do,” Dr. Blair, who wrote a book on nuclear command and control, said in an interview. “He has no authority to refuse or disobey that order.”And as long as we're consulting the Grey Lady, this piece by former CIA director Michael Morell is also worth noting:
During a 33-year career at the Central Intelligence Agency, I served presidents of both parties — three Republicans and three Democrats. I was at President George W. Bush’s side when we were attacked on Sept. 11; as deputy director of the agency, I was with President Obama when we killed Osama bin Laden in 2011.
I am neither a registered Democrat nor a registered Republican. In my 40 years of voting, I have pulled the lever for candidates of both parties. As a government official, I have always been silent about my preference for president.
No longer. On Nov. 8, I will vote for Hillary Clinton. Between now and then, I will do everything I can to ensure that she is elected as our 45th president.
Two strongly held beliefs have brought me to this decision. First, Mrs. Clinton is highly qualified to be commander in chief. I trust she will deliver on the most important duty of a president — keeping our nation safe. Second, Donald J. Trump is not only unqualified for the job, but he may well pose a threat to our national security. [Emphasis added.]Worth reading the whole thing.