* Chevron warns on Q3 earnings
* Initial jobless claims rise on technical problems
* Citrix Systems tumbles after outlook
* Indexes up: Dow 1.21 pct, S&P 1.25 pct, Nasdaq 1.50 pct
By Chuck Mikolajczak
NEW YORK, Oct 10 (Reuters) - U.S. stocks rallied strongly at the open on Thursday, with each of the major indexes climbing more than 1 percent, as investors were encouraged by signs of progress in fiscal negotiations in Washington.
According to a Republican leadership aide, U.S. House Republicans are considering agreeing to a short-term increase in the government's borrowing authority, keeping a possible default after Oct. 17 at bay and buying time for negotiations on broader policy measures.
President Barack Obama and congressional leaders are set to meet Thursday for further discussions.
"It would be a minor sign of hope there may be some more positive news coming in the next couple of days, hard to make much more out of that," said Fred Dickson, chief market strategist, D.A. Davidson & Co. Lake Oswego, Oregon.
"The markets right now are betting somebody will blink between now and October 17."
The U.S. government shutdown has been in effect for ten days since congressional Republicans refused to pass a budget for the fiscal year without modifications to Obama's healthcare reform law.
U.S. Treasury Secretary Jack Lew said the gridlock in Washington was hurting the U.S. economy, and urged Congress to raise a cap on government borrowing to keep America from defaulting on its debt.
Initial claims for state unemployment benefits increased 66,000 to a seasonally adjusted 374,000, the highest since the end of March and well above expectations for 310,000 claims, though technical problems in California from computer upgrades were responsible for half the increase in claims.
The Dow Jones industrial average rose 179.56 points, or 1.21 percent, to 14,982.54, the S&P 500 gained 20.74 points, or 1.25 percent, to 1,677.14 and the Nasdaq Composite added 55.29 points, or 1.5 percent, to 3,733.066.
This year's high-flying tech stocks - such as Facebook Inc , up 3.2 percent at $48.28, and Amazon.com Inc, up 2.3 percent at $305 - rebounded after several days of declines.
The Nasdaq technology sector was up 1.1 percent after having shed 2.8 percent over the last three sessions, its biggest three-day drop since late June.
Chevron Corp, fell 0.6 percent to $115.45 as the biggest drag to the Dow after the second-largest U.S. oil company warned Wednesday its third-quarter earnings would be lower than in the second quarter as fuel margins were squeezed.
Gilead Sciences Inc gained 4.4 percent to $61.47 as the biggest boost to the S&P 500 after a pivotal trial of its drug idelalisib was determined by independent monitors to be effective against Leukemia and was stopped early. The NYSEArca biotech index climbed 2.4 percent.
Citrix Systems Inc slumped 11 percent to $59.32, making it the worst performer on the benchmark S&P index after the cloud computing software maker estimated quarterly results to be below analysts' expectations as businesses delayed contracts.