Officials told Reuters that deputies in Ivano-Frankivsk region, in western Ukraine, had sent the draft back to the government, pressing for guarantees which would address their concerns over the exploration plans.
Chevron wants to tie up a deal to explore the Olesska shale field in western Ukraine. Royal Dutch Shell has already signed a $10 billion (€7.45 billion) deal for shale exploration and extraction at the Yuzivska field in the east of the ex-Soviet republic.
According to the council's website, deputies expressed concerns over the ecological consequences of shale exploration in the mountainous forest region which is known for inland tourist resorts.
The "fracking" process, in which water and chemicals are used to break up rock, sandstone and shale deposits to release gas, has sparked opposition from environmentalists elsewhere in Europe who fear it can pollute underground water.
But the Kiev government sees shale gas development as important for easing its dependence on costly gas imports from Russia which weigh heavily on its economy.
Fuel Minister Eduard Stavytsky was quoted by UNIAN news agency as saying that Chevron has proposed investing $350 million (€260 million) in initial tests to ascertain the commercial viability of gas deposits at the Olesska field, with a $3 billion (€2.23 billion) investment envisaged for the first stage of extraction.
Stavytsky told Reuters by telephone: "We will consider the proposals (from the council) and in mid-September there will be another vote.
"There is nothing dramatic in what has happened. This is the normal working process," he said.
"Chevron looks forward to understanding how the Ukrainian government plans to address the concerns raised by the Ivano-Frankivsk Regional Council which will enable us to move forward expeditiously to implement this strategic project," a Chevron spokeswoman said.
In the council debate, Iryna Sekh, a national deputy from the Svoboda far-right nationalist opposition, said: "This agreement opens the way to lawful destruction of Ukrainian land during gas extraction.
"There are clauses in the agreement which allow Chevron to turn hundreds of kilometres of Ukraine into swamp and desert. Chevron would have the right to use sand, stone, underground water supplies and other water sources on the basis of agreements in and beyond the (agreed) area.
"I doubt that there is a country in the world which would allow such rights and privileges to a foreign investor," she said.
Even if the Ivan-Frankivsk council eventually supports the deal, it would still require the approval of a second council in the Lviv region.