Chris may eventually impact parts of Nova Scotia and Newfoundland while transitioning into a strong non-tropical area of low pressure late in the week.
The Bermuda Weather Service warned it may move closer after that, depending upon its track.
While Chris is expected to become a hurricane, it will stay offshore and head to sea, according to the storm center.
There was high threat of unsafe rip currents north of Cape Lookout, according to the National Weather Service's Newport/Morehead City office.
Barbadians can breathe a sigh of relief, as the island is no longer under Tropical Storm Watch.
The Atlantic hurricane season, which runs from June 1 to November 30, spared Bermuda a year ago, but battered the Caribbean as well as the United States. It was centered 60 miles (95 kilometers) east of Martinique and was racing west-northwestward at 26 mph (43 kph).
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Maximum sustained winds are near 45 miles per hour (75 km/h) with higher gusts.
Tropical storm watches were in effect for Barbados, St. Lucia and Dominica.
As of Sunday evening, Chris was about 180 miles south-southeast of Cape Hatteras, North Carolina, with maximum sustained winds of about 50 mph.
By Tuesday, the storm is forecast to degenerate but could still produce some gusty winds and heavy rain over Puerto Rico and Hispaniola.
Tropical Storm Beryl is moving rapidly westward toward the Lesser Antilles at the eastern entrance of the Caribbean Sea.
About 7,000 houses and businesses in Puerto Rico still lack power after Hurricane Maria leveled an electricity grid that was ill-maintained before the storm.