As of Monday afternoon, Chantal was centered about 550 miles east-southeast of Barbados and was moving west near 25 mph.
The storm's maximum sustained winds were near 45 mph with some strengthening expected over the next two days.
"It's on a path to pass over Cuba later this week and then the Bahamas by the weekend," Local 6 meteorologist Troy Bridges said. "Some models then show it skirting along Florida's east coast."
A tropical storm warning has been issued for Puerto Rico, Barbados, Dominica, St. Lucia, Martinique and Guadeloupe. A tropical storm watch is in effect for St. Vincent.
Chantal is expected to produce 2 to 4 inches of rain over the Leeward and Windward Islands with a maximum amount of rain expected at 6 inches.
Meanwhile, there's a 20 percent chance of rain in Central Florida on Monday and Tuesday.
High temperatures will be in the low 90s, and overnight lows will be in the mid-70s.
Rain chances increase to 40 percent from Wednesday through Sunday.
In the Pacific, Tropical Storm Erick is nearing the southern portion of Mexico's Baja California peninsula, where a tropical storm warning is in effect.
Erick's maximum sustained winds have decreased to near 50 mph with gradual weakening expected to continue over the next two days.
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