Transocean Ltd., owner and operator of the Deepwater Horizon drilling rig that burned and sank last month and unleashed a massive oil leak into the Gulf of Mexico, on Thursday filed a request in court to limit its liability to just under $27 million.

While the world's biggest offshore driller may not succeed in limiting its financial liability, the filing could give Transocean an edge in what could be a lengthy, multipronged legal battle against claims for damages from the accident that killed 11 workers.

"One...