UPDATE 2-Chevron starting to buy back its shares

* Buybacks stopped in January 2009 amid financial crunch

* Larger rival Exxon ramping up its repurchase program

* Chevron shares up 0.8 pct in after-hours trading (Adds background, Exxon buybacks; updates share price)

HOUSTON/SAN FRANCISCO, Oct 4 (Reuters) - Chevron Corp (CVX.N) plans to resume quarterly buybacks of up to $1 billion of its own stock after a nearly 2-year halt as the second-largest U.S. oil company grows more confident about its finances.

"Initiating repurchases at this time is evidence of our ongoing capital discipline and strong cash flows, including from newly developed oil and gas projects," Chief Financial Officer Pat Yarrington said in a statement on Monday.

Yarrington, in her first big act after being promoted to CFO in January 2009, had halted Chevron's repurchases in the thick of a financial crunch that also led larger rival Exxon Mobil Corp (XOM.N) to scale back its buyback program.

Exxon is slowing ramping up the program again, saying in July it expected to repurchase $3 billion of shares in the third quarter after doing $4.1 billion worth in the first half -- excluding the impact of its XTO takeover. That compares with Exxon's $8 billion of buybacks in the last quarter of 2008.

Chevron's share repurchase program, previously authorized by its board of directors, will start this quarter and run at a rate of $500 million to $1 billion every three months.

Asked about resuming buybacks in April, Yarrington had said she was not ready to look at it. Since then, Chevron has increased it 2010 production target to 3 percent growth from 1 percent, and U.S. oil prices have averaged above $75 per barrel, compared with just over $41 when the buybacks stopped.

After the announcement, shares of the San Ramon, California company reversed their regular-trade decline of 0.8 percent, rising to $82.00 in after-market trading. (Reporting by Braden Reddall in San Francisco and Anna Driver in Houston; Editing by Richard Chang)