On 4 October 1957 the Soviet Union took the lead in the Space Race by launching Sputnik I, the first successful artificial satellite.
One of several plans by the the US government to reverse this embarrassment, given the failure of the their own Project Vanguard satellites, was to detonate an atomic bomb on the Moon. This was known as Project A119 – “A Study of Lunar Research Flights”. The resulting flash would be visible from Earth, boosting the morale of the American people.
There were intelligence reports that the Soviet Union had a similar plan and that they would time the explosion to occur during a lunar eclipse in 1957 to celebrate the anniversary of the October Revolution.
Not surprisingly, Project A119 did not go ahead as it was considered there might be an unfavourable public reaction to nuking the Moon.
A young Carl Sagan worked on the Project and it is through his biographies that the project is known about at all.
The project report can be found here: A Study in Lunar Research Flights
Image: Photo courtesy of National Nuclear Security Administration / Nevada Site Office [Public domain], via Wikimedia Commons