Nearly 70 percent of the members the council in Lviv in western Ukraine approved the preliminary agreement with Chevron, the Ukrainian News Agency reported.
The report said the Lviv council's action drew shouting protests by opposition groups equating hydraulic fracturing to the Chernobyl nuclear disaster in Ukraine in 1986. Some of the chemicals used during hydraulic fracturing, dubbed fracking, are viewed as a threat to groundwater.
Ukraine is one of the Eastern European countries thought to be rich in shale natural gas.
In January, Royal Dutch Shell signed a $10 billion contract to explore Ukrainian shale. In July, British-based exploration and production company JKX Oil & Gas said it started a multistage hydraulic fracturing operation it said was likely the largest operation of its kind in Europe to date
Ukrainian Prime Minister Mykola Azarov said there may be enough natural gas in shale plays to meet the country's needs without imports.