* NanoBio gets $14.5 mln upfront, milestones up to $40 mln

* Deal covers over-the-counter use of U.S. firm's NB-001

(Adds product details, Glaxo strategy, background)

LONDON, Dec 16  - GlaxoSmithKline (GSK.L) took a further step to build up its non-prescription consumer health business on Wednesday with a small deal giving it rights to an experimental cold sore treatment from privately owned NanoBio.

The U.S. company will get an upfront payment of $14.5 million and is eligible to receive additional milestone payments of up to $40 million plus single digit royalties on future sales.

In return Glaxo will have exclusive rights to sell NanoBio's NB-001 product -- due to enter final Phase III testing soon -- as an over-the-counter treatment in the United States and Canada.

Glaxo has already established Abreva as the leading cold sore treatment with a greater than 50 percent market share but its sees NB-001 as the next advance in tackling the condition, which is caused by the virus herpes labialis.

The British company's Consumer Healthcare division is one of the world's largest over-the-counter health businesses, with a range of products covering everything from smoking cessation to toothpaste.

It is a priority growth area for Glaxo's chief executive, Andrew Witty, who wants to reduce its reliance on volatile sales of traditional prescription drugs in Western markets. (Reporting by Ben Hirschler; Editing by Greg Mahlich)