Chevron (CVX -0.79%) reported its third-quarter results this morning, with earnings falling 5.8% from year-ago levels to $4.95 billion. Yet the oil giant's revenue climbed by 0.8% to $58.5 billion, and rising production levels in both oil and natural gas helped ease concerns about Chevron's growth prospects.

Unlike rival ExxonMobil (XOM -3.72%), which posted mixed results among its internal divisions, Chevron saw net income drop in both its upstream and downstream operations. Upstream earnings from Chevron's exploration and production businesses fell by almost 1%, with a sharp decline in income from the U.S. side of the segment more than offsetting slight gains internationally. But downstream operations from refining and marketing took a much bigger earnings hit, with net income from the segment dropping 45%. Foreign-currency effects also continued to hold Chevron's earnings down, as the company attributed $276 million in lost earnings to the strong dollar.

On the production side, though, Chevron posted solid gains. Total production rose by 2.7%, with growth coming equally from domestic and international projects. Natural gas production growth outpaced Chevron's overall production growth rate, although the 2.2% gain in oil and liquids production reversed drops earlier in the year on that side of the business.

Chevron CEO John Watson blamed the earnings drop on lower refinery margins but cited "good progress on our major capital projects," including its construction of liquefied-natural-gas plants in Australia and its deepwater efforts in the Gulf of Mexico, as reason for optimism. Watson also pointed to growth opportunities in Chevron's downstream business.

As of 9:10 a.m. EDT, Chevron shares were down about 0.5% in pre-market trading.

Chevron will have a conference call at 11 a.m. EDT to discuss the results in further detail. For more information, visit the Chevron investor relations site.