Greaves was 64 not out and Chase on 36 when bad light stopped play after 74 overs. Greaves previously put on 53 for the fifth wicket with Shai Hope (29) as West Indies showed resilience on a turning pitch on Sunday.
Pakistan looked at the conditions before the start of play at Queen's Park Oval and made the surprising decision to leave out veteran pacer Mohammad Abbas who took eight wickets in the first Test.
West Indies won the toss, chose to bat and opener Brandon King provided the hosts with an aggressive start, scoring 46 from 50 balls.
King put on 49 with Tagenarine Chanderpaul (15) for the first wicket in a morning session in which only 9.5 overs were bowled because of rain.
West Indies was tested in an extended second session in which the ball began to turn sharply and three early wickets fell. Through Greaves, Hope and Chase, West Indies managed to battle to a position at stumps which rewarded the decision to bat first.
Pakistan's bowlers often were let down by their fielders, but also by the apparent lack of a clear plan which could be supported by field settings.
At stumps, Mohammad Ali had done best with 2-49 while Ubaid Shah, who conceded 56 runs from nine overs, and spinners Ali Usman and Sajid Khan had a wicket each.
King particularly punished Shah's inconsistency in his opening spell, taking seven of his nine boundaries from the young right-armer.
Pakistan rallied when play resumed after lunch as Usman removed King. Kavem Hodge (10) and Amir Jangoo (26) then fell to catches by Mohammad Rizwan behind the stumps from the bowling of Khan and Shah respectively.
West Indies was 4-120 at that point but Hope began the fightback with his dogged 29 from 68 balls before he was bowled by Mohammad Ali shortly after tea.
Greaves reached his half century from 92 balls. With Chase, he steered West Indies through the shortened final session without further loss, putting it in a strong position on a pitch on which run-scoring might become more difficult.
Earlier, West Indies kept the same team who won the opening Test at Tarouba by 90 runs.
Pakistan captain Babar Azam said at the toss that Abbas was left out because of the conditions, with Shah awarded his Test debut.
Abbas was one of four changes for Pakistan. Shan Masood, a century-maker at Tarouba, has a fractured left index finger. He was replaced by Abdullah Shafique.
