The New Zealand cricketers are 146 for 8 in their second innings, giving them a lead of 392 runs midway through the 4th day of the opening Test against the West Indies in Jamaica.
Opener Tom Latham has just been dismissed for 73, while BJ Watling is on 19.
Earlier night watchman Ish Sodhi made 4, Ross Taylor a golden duck, Brendan McCullum 17, Jimmy Neesham 20 and Tim Southee 3.
Pace bowler Jerome Taylor has 4 wickets.
The West Indies biggest ever successful run chase was 418 for 7 against Australia in 2003.