Management has repeatedly said the company has the resources to preserve the dividend until 2017 and the market agrees.
Chevron's dividend yield of 5.5% does not exactly scream 'dividend cut'. Chevron has one of the lowest debt to equity ratios in the industry, with a debt ratio of 17.1% as of 6/30/2015.
Management has identified $3 billion in cost reduction opportunities and is cutting capital expenditures. Management is also divesting non-core assets to balance its cash flows.