Can traditional supermarkets, like King Kullen, continue to hold their own against the growing onslaught of the discounters and a relatively new and ferocious German upstart, Aldi, which is spawning new outlets on Long Island and elsewhere faster than sales of lemonade on a hot day.

King Kullen, the Hauppauge-based supermarket chain — and America’s oldest grocer — is placing its bets on Tracey Cullen, the 46-year-old great-granddaughter of the company’s founder, Michael J. Cullen. This spring, she was named president and chief operating officer of the company that got its start with one store in Jamaica, Queens, in 1930.

Cullen, an attorney who most recently served the company as senior vice president for company operations, is King Kullen’s first woman president. She replaces Joseph W. Brown, who has retired after a 53-year career with the company. Brown was president and COO for the past five years.

King Kullen, is a familiar shopping destination to many Long Islanders. The company has 24 locations and four Wild by Nature stores, which focus on organic foods, natural products, and healthier grocery options. The first Wild by Nature store opened in East Setauket in the mid-1990s.

Cullen, the daughter of former King Kullen co-president Brian C. Cullen, practiced law at a New York City labor and employment firm. She joined King Kullen in 2010 and lives in Amityville. Her appointment to head the company was announced by her uncle, King Kullen chairman James A. Cullen Jr.

“This is a special day for the King Kullen organization,” Cullen said in a statement. “Over the years, my niece has taken on leadership roles of increasing responsibility and has played an important part in helping shape the company’s future.”