(Reuters) - U.S. supermarket chain Albertsons Companies Inc is in advanced talks to acquire closely held grocery store operator Price Chopper for around $1 billion, people familiar with the matter said on Tuesday.

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A deal would underscore the wave of consolidation sweeping the U.S. grocery industry, as regional chains struggle to compete against online retailers such as Amazon.com Inc AMZN.O, big box stores such as Wal-Mart Stores Inc WMT.N, and discount chains such as ALDI Inc.

These challenges put pressure on the Golub family, which has owned Price Chopper for more than eight decades, to explore a sale. Lewis Golub, a Russian immigrant who arrived at New York’s Ellis Island in 1900, started a wholesale grocery warehouse in 1922, which his two sons launched as a supermarket chain in 1932.

The sources, who asked not to be identified because the matter is confidential, cautioned that it is still possible for the deal negotiations to fall through. Albertsons and Price Chopper declined to comment.

Schenectady, New York-based Price Chopper operates roughly 130 stores across the U.S. Northeast, including New York, Connecticut and Massachusetts. Earlier this year, Scott Grimmett took over from Jerry Golub as chief executive of Golub Corp, the Golub family’s company. He is the first non-family member to hold that position.

Boise, Idaho-based Albertsons, which is controlled by private equity firm Cerberus Capital Management LP and operates more than 2,200 supermarkets, is the second largest U.S. grocery chain after Kroger Co KR.N. In a sign of how fragmented the U.S. grocery market is, these two companies, together with Publix Super Markets, controlled just 27 percent of the market in 2015, according to research organization IBIS World.

Earlier this year, Dutch supermarket group Ahold AD.AS and Belgian peer Delhaize merged, combining two of the U.S. Northeast's strongest competitors, Quincy, Massachusetts-based Stop & Shop and Scarborough, Maine-based Hannaford.

In 2015, Albertsons combined with Pleasanton, California-based Safeway, in a $9.2 billion merger that expanded its presence in the central and western U.S.

The company’s other supermarket brands include Vons, Jewel-Osco, Shaw’s, Tom Thumb and United Supermarkets. Albertsons filed with the U.S. Securities and Exchange Commission for an initial public offering in July 2015, but has yet to go public.

(This story corrects to remove reference to Harris Teeter in eighth paragraph)