Shake Shack, the New York City burger stand whose frozen custard has gained a fierce following, plans to open its first Massachusetts store next year at the Chestnut Hill Shopping Center. Shake Shack will take over roughly 3,000 square feet in the Boylston Street space formerly occupied by the Rugged Bear children’s store, where it will feature its signature line of burgers, hot dogs, and frosty treats. “With its proximity to Boston College, Chestnut Hill is a thriving community to bring Shake Shack,’’ said Randy Garutti, Shake Shack’s chief executive.
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