After Brathwaite made 86 at the top of the innings, Chase scored an unbeaten 91 to take the West Indies to stumps on 369 for eight.
Although Zimbabwe ended the day with the wicket of Devendra Bishoo for 44 to gain sight of the end of the tourists' second innings, they will now need to achieve a world record chase to win the match.
Captain Graeme Cremer was the most successful bowler on the day, ending with figures of 3 for 111.