37-year-old Chambers revealed the family's location in an Instagram post on Thursday.
She wrote, "Left home yesterday for the first time in almost a month for our second grocery run and the experience was drastically different than before."
"We're currently quarantined in the Caymans, which wasn't planned when we left LA 5 weeks ago for NYC for previews of @minutesbway [Armie's play]. Due to travel restrictions, school closures and the fact that we were planning to be here with our extended family two weeks later for spring break, we made this decision for the health and safety of our family," Chambers.
She further explained how the government in the Cayman Island is enforcing strict "curfews, lockdowns and visitation to essentials businesses."
"It seems to be working," she said. "There are no lines or crowding and when I asked the cashier if they have been busy/overwhelmed on the weekends, she said that it's never very busy and no lines because of the mandates."
For the Hammer family, the Caymans is a special place as Armie's family moved there when he was seven years old, and he lived there for five years before returning to Los Angeles.
In a 2018 interview, Hammer said of the Caribbean island, "It's been such a huge part of my identity and what I consider my formative years."
Armie and Elizabeth got married in 2010 and they have two kids: 5-year-old daughter Harper and 3-year-old son Ford.
( With inputs from ANI )