The signs were everywhere: The steady stream of human traffic from New York’s Chinatown to the Fifth Avenue Apple Store. The housewives arrested at the Hong Kong crossing with dozens of units strapped under their dresses. The scalper fights that broke out when Apple’s Beijing store briefly lifted its two-iPhones-per-customer limit.

No wonder Apple (AAPL) decided several years ago to make China its “top priority” among the BRIC (Brazil, Russia, India, China) countries. “We put enormous energy in China,” COO Tim Cook told analysts this week, “and the result of that has been absolutely staggering.”

The chart at right shows the sharp growth in Apple’s Asia Pacific revenues — a number Apple didn’t even bother to break out in its SEC filings until 2008 (it was tossed into the “Other Segments” basket along with sales of FileMaker). Today, according to Morgan Stanley’s Katy Huberty, Asia Pacific is the company’s largest earnings driver, representing 39% of the company’s operating income growth last quarter.

Within that market, Cook reported, revenue from greater China totaled $2.6 billion in Q1 2011, four times the revenue from the same quarter last year.

Although China is the world’s biggest market for mobile phones, not all of China’s 1.3 billion citizens can afford an iPhone. But Huberty estimates that there is a core addressable market of 50 million middle-class Chinese with plenty of disposable income and a “strong interest in smartphones and the Apple brand.”

This is the market Apple was targeting when it announced that it planned to build 25 Apple Stores in China within the next two years. Four of those stores have already opened and they draw, according to Apple, more traffic and generate more revenue than any other Apple Stores in the world.

Ironically, because the phones are manufactured on mainland China, Apple can’t make iPhones fast enough to meet the country’s demand. Ticonderoga Securities’ Brian White, back from a recent tour, reported in December that the iPhone 4 had been sold out for two months. He estimated that China Unicom (CHU) was unable to fulfill about a third of its orders.

“We continue to believe,” White wrote, “that China remains in the early stages of catching ‘Apple fever.'”

See also:

• China’s iPad-smuggling housewives
• iPhone chaos in Beijing
• Coming soon: 4-5 million Chinese iPhones
• China iPhone launch a ‘disappointment’
• Inside Beijing’s iPhone black market

[Follow Philip Elmer-DeWitt on Twitter @philiped]