(CNN)As countries ravaged by the coronavirus rushed to vaccinate their populations earlier this year, there was little sense of urgency to get inoculated in Taiwan.

The island of 23 million people had recorded close to zero local infections for months, and demand for the vaccine was so low that only 1% of the population was vaccinated.

But in this pandemic things can change quickly. Today, Taiwan is battling its worst outbreak yet, reporting more than 1,000 new cases in the past week, and has a population that wants the vaccine -- but can't get it.

Now, the Taiwanese government is asking the United States for a share of the shots President Joe Biden plans to send abroad, as it waits for other deliveries to arrive.

But in theory, there could be a solution for Taiwan right on its doorstep: Chinese vaccines.

China has sent tens of millions doses of its domestically developed vaccines around the world. But tensions across the Taiwan Strait have run high since the pandemic, with Beijing blocking Taiwan's participation at the World Health Organization, courting Taipei's dwindling allies and ramping up military pressure on the self-governed island, which it considers part of its territory.