Boyko was one of the main forces behind negotiating that agreement in November, and he currently plays a mediating role on energy matters between the governments of Ukraine and Russia. He put Chevron's expected exploration investment at $350 million, within two areas of western Ukraine.
Van Ast said that Chevron's efforts are ongoing despite serious unrest in Ukraine, especially in the eastern part of the country. "We are monitoring the situation, but we continue to have a team in Ukraine who are engaging with key stakeholders on a daily basis," Van Ast said.
Royal Dutch Shell is currently the biggest player in the Ukrainian market. The company declined to comment on specific dollar figures, but said that it has ongoing operations in the region.
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Shell spokesman Curtis Smith told CNBC that it employs about 2,500 people in Ukraine, many as contract workers. The company is involved in two exploration projects, both in eastern Ukraine, including in the Donetsk and Kharkov regions, the most troubled in the country.
To date, the company said operations have not been affected despite rising tension in those areas.
"We continue to prepare for exploration activities on Yuzivska area," Smith told CNBC. "We monitor trade controls and sanctions closely and will respond appropriately to ensure that we comply with all applicable international sanctions and related measures."