Tensions over the dispute have reached such a level that a Malaysian navy patrol boat recently chased a Total exploration vessel away from the area. The company has since stopped all offshore work at the disputed Block J.
Block J is one of two deepwater blocks that are considered important to help Brunei maintain its current levels of oil and gas output in the future.
The country currently relies on oil and gas sales for 75% of its revenue and Brunei Shell Petroleum, the country's largest oil and gas producer, is expected to see production levels fall at several of its shallow-water blocks over the coming decade.
Brunei also claims the area is wholly within its Exclusive Economic Zone (EEZ), which stretches 200 nautical miles out from its shore, in a northwesterly direction.
A profit-sharing development contract for block J was awarded in 2002 by the Brunei government, and was signed in April by Total, BHP Billiton and Amerada Hess (AHC).
The dispute is the latest in a series of sovereignty claims in the region involving Malaysia.
In December, Malaysia won an International Court of Arbitration ruling over Indonesia on the ownership of Sipidan and Ligitan islands off Sabah, on the other side of Borneo from the area it disputes with Brunei.
Malaysia and Singapore are also currently in legal wrangles over the sovereignty of the tiny Pedra Blanca island, north-east of Singapore.
The ongoing dispute between Malaysia and Brunei is expected to be a long-dragged out affair, with no quick solution in the horizon. The dispute may have to be sorted out in an international court if both governments fail to come to an agreement.