The Kulluk drilled in the Beaufort Sea off Alaska's north coast during the 2012 open water season.
It was being towed to Seattle for maintenance and upgrades Dec. 27 when its tow line broke.
Reattached lines also broke, and the vessel ran aground New Year's Eve.
A Shell towing vessel pulled the barge off the rocky bottom Sunday night and towed it Monday to a sheltered Kodiak Island bay.
Begich, an Alaska Democrat, is chairman of the Senate Subcommittee on Oceans, Atmosphere, Fisheries and the Coast Guard. No date for the hearing has been set.
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