* Deal faces opposition from local councils, far-right group
* Ukraine hopes shale gas will ease its dependence on Russia
KIEV, Jan 29 (Reuters) - Ukraine has removed a self-imposed May 2013 deadline on signing a shale gas deal with energy major Chevron which faces scrutiny in local councils dominated by opposition groups, a government document showed on Tuesday.
The former Soviet republic is seeking to ease its dependence on costly natural gas supplies from Russia and signed a landmark production sharing agreement with Shell this month that could bring in $10 billion in investment.
But the move on Tuesday indicated that the government had no quick plan to overcome domestic opposition to the second large shale gas deal and its approval could be delayed significantly, casting doubt on the whole project.
Ukraine is said to have Europe's third-largest shale gas reserves at 42 trillion cubic feet (1.2 trillion cubic metres), according to the U.S. Energy Information Administration.
The Kiev government picked Shell and Chevron as partners to develop the Yuzivska area in eastern Ukraine and Olesska area in western Ukraine, respectively, through a tender last May.
Ukraine estimates the reserves of the Olesska area at 0.8 to 1.5 trillion cubic metres.
But whereas local councils in the eastern Donetsk and Kharkiv regions, loyal to the ruling Party of the Regions, quickly approved the Shell deal, opposition groups that dominate western Ukrainian councils threaten to block the Chevron one.
The far-right nationalist Svoboda party, which surged on to the political landscape in parliamentary elections in October, is strong in the west of the country and opposes shale gas exploration citing environmental concerns.
Shale gas technology uses a process called "fracking" in which fluid and chemicals are injected at high pressure into beds of rock, often situated deep in the ground, to access gas reserves trapped there.
Critics say fracking could contaminate water and cause other environmental issues.
The government decree adopted last month and published on Tuesday removes the May deadline for signing the deal but does not set any new term for its conclusion.
Developing shale gas reserves is a key element in Ukraine's strategy aimed at securing energy independence. Kiev's current deal with Russia sets an exorbitant price for gas - about $430 per thousand cubic metres this quarter, - Ukraine says.
Kiev's attempts to renegotiate the deal have so far failed.
Straining the bilateral relations even further, Russia this month sent Ukraine a $7 billion bill for the gas that it says Kiev was obliged to buy but never bought as it tried to reduce imports last year.