They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
West Indies won the toss and elected to bowl under heavy skies, picking up the wickets of Hashim Amla (6) and Aiden Markram (5), both off the bowling of seamer Sheldon Cottrell (2-18).
Quinton de Kock (17 not out) and captain Faf du Plessis, who has yet to score, are at the crease for South Africa, who lost their opening three games of the tournament and are in desperate need of victory or face an embarrassing early elimination.
Rain had been predicted throughout the day in Southampton, with the outfield already slow, making scoring boundaries more difficult.