UPDATE 1-Kyushu Elec: may not be able to meet power demand

* Could fail to meet demand if oil-fired unit stays shut

* Ainoura unit closed this afternoon due to boiler problem

* Utility has no nuclear reactors online (Recasts on company confirmation, adds detail)

TOKYO, Dec 26 (Reuters) - Kyushu Electric Power Co said on Monday it may fail to meet power demand in January if the shutdown of the 500-megawatt oil-fired No.2 unit at its Ainoura plant in southwestern Japan is prolonged.

The southern Japan company, one of the country's most nuclear reliant regional utilities, has no reactors online amid public concerns in the wake of the Fukushima atomic crisis.

It said it would only be able to supply 14,190 megawatts of power in January if the unplanned shutdown of the oil-fired unit continued, falling 2.6 percent short of estimated peak demand of 14,570 MW.

Kyushu Electric is asking users to voluntarily cut peak-hour power use by five percent or more until Feb. 3 to avoid unexpected blackouts.

The Ainoura unit was shut this afternoon due to a problem in a boiler, and it is not yet clear when it will be able to restart, said a spokesman for the utility. (Reporting by Kaori Kaneko and Risa Maeda; Editing by Joseph Radford)