In today's world, there is a great deal of pressure on firms such as Chevron to show that they care about something other than making a profit. If they can show this, they can improve their image and, thereby, may be able to improve their market share.
In order to show this, Chevron should make a point of funding "green" initiatives and research. The company should make a point of showing that they are trying to make their own operations more environmentally friendly and that they are trying to help improve/conserve the economy in other ways as well. If possible, Chevron might want to branch out and start investing in clean energy technologies. All of these actions would convey to the public the idea that Chevron cares about the environment and is doing everything that it can to help preserve it. In this way, Chevron could project a responsible image, one which can help it to maintain or improve its market share and profitability.