By Ellen Wulfhorst

NEW YORK, Oct 31 (Reuters) - A group of Barclays Center luxury box holders sued the giant events center in Brooklyn on Thursday, claiming they have been treated badly because they are black.

The federal lawsuit filed by Ludwig's Drug Store, which seeks $4 million in damages, claims its manager and two other staffers who bought into the box have been "harassed, followed and questioned."

The three men say they are the only black box holders at Barclays, which opened in September 2012 and can hold as many as 19,000 people. It has 101 luxury suites, according to its website.

The Brooklyn-based drug store signed a three-year lease for nearly $1 million for a luxury box three weeks ago, according to the lawsuit.

Since then, the three say in the lawsuit they have been treated with suspicion, ignored by staff, forced to wait long times for orders that sometimes never arrive and once were billed $1,000 for a pizza that arrived late and was cold. Their luxury box is rarely cleaned, they say.

The complaint is the latest in a string of accusations of racism at commercial spots in New York.

Several black customers complained in recent days that they were stopped by police after making luxury purchases at Barneys New York and at Macy's Inc, and Barneys and the police were named in a lawsuit filed by a student who said he was detained after buying an expensive belt.

The complaints against the stores have prompted an investigation by the state attorney general into their security practices.

The treatment by Barclays is "unlawful discriminatory practice because of race," said the lawsuit filed in U.S. District Court in Brooklyn.

Barclays spokesman Barry Baum said in a statement that it would "immediately and thoroughly" investigate the claims.

"We have a zero tolerance policy for any type of discriminatory behavior. It is against everything that Barclays Center stands for," Baum said, noting that Barclays had not received legal papers nor complaints from the box holders.

The attorney representing the three men declined to speak to the media, his office said.

In the year since it has opened, Barclays has hosted shows by such top performers as Jay Z, Barbra Streisand, the Rolling Stones and Paul McCartney. It is home to the Brooklyn Nets and will be home to the New York Islanders professional hockey team starting in 2015.