At 8 a.m. EDT, the storm had maximum sustained winds of about 35 mph, 4 mph below the threshold for a tropical storm. Forecasters said it might creep up to tropical storm strength again but wouldn't go much farther than that.
"It's going to be hard for it to strengthen to a hurricane within the next five days," meteorologist Robbie Berg said at the National Hurricane Center in Miami.
Forecasters expected Chris to head over Cuba and into the Gulf of Mexico, reaching Texas or Mexico by early Wednesday.
Early Friday, the depression's center was about 20 miles south of Grand Turk Island in the southwestern Bahamas and was moving west at about 13 mph. It was expected to pass over Haiti, the Dominican Republic and the southeastern Bahamas on Friday with anywhere from 2 to 6 inches of rain.
Puerto Rico's Fajardo River spilled its banks Thursday afternoon and sent water gushing over a highway, temporarily shutting down the road in the U.S. territory's northeast coast as the storm moved swept past the island.
There were no reports of major damage elsewhere in the Caribbean from Chris, which on Wednesday had threatened to become the first hurricane of the Atlantic season.
A tropical storm warning was in still in effect for the southeastern Bahamas and the Turks and Caicos Islands. The warning included the Acklins, Crooked Island, The Inaguas, Mayaguana and the Ragged Islands.
Long Island and the Exumas in the central Bahamas were under tropical storm watches. Watches were canceled for Samana, the Dominican Republic and the northern coast of Haiti to La Mole St. Nicolas.