WASHINGTON — The Nuclear Regulatory Commission voted 4 to 1 on Thursday to grant a license to build and operate two reactors at a nuclear plant in Georgia, a crucial threshold for an industry that has not had a new start since 1978.

The $14 billion project, of which $4 billion was already spent on steps like digging a foundation and laying water pipes, will be closely watched by utilities around the country, many of which are leery of nuclear construction because of huge cost overruns in the last round of construction in the 1960s, ’70s and ’80s.

At the same time, many are intent on seeking an alternative to natural gas, the fossil fuel now dominating construction plans.

The Southern Company is adding the two reactors to its Alvin W. Vogtle nuclear plant near Augusta, in tandem with several partners that serve municipal utilities or electric cooperatives.