Two workers died after January 16 explosion at the KS Endeavour exploration rig, chartered by the US firm for work at its offshore Funiwa oil field.
Friends of the Earth says this is the world’s worst such accident in recent years.
Chevron spokesman Lloyd Avram says, despite the fire, the situation is now under control and no oil is leaking.
Nigeria is the largest oil producer in Africa.
The fire at the Funiwa field is burning in a 40m-wide area on the surface of the Atlantic Ocean, 10km off the Nigerian coast.
The company is trying to put out the fire by piercing a hole in the original gas well – through which cement will be poured.
“There’ll be 10,000ft of drilling and interestingly we need to hit an area that is approximately 12sq inches,” Mr Avram told the BBC.
“It is going to take some time, but I cannot predict how long that is going to be – conceivably months,” he said.
Scientists are conducting tests to find out if local food and water has been contaminated by the gas in the ocean – after local people raised concerns.
Almost 100 people have left towns close to the fire and local chiefs are asking Chevron to relocate more.
A major build-up of gas pressure from drilling caused the explosion that set the rig on fire in the middle of January, according to state-run Nigerian National Petroleum Corporation (NNPC).