The acyclic point-connectivity of a graph G , denoted α ( G ) , is the minimum number of points whose removal from G results in an acyclic graph. In a 1975 paper, Harary stated erroneously that α ( Q n ) = 2 n − 1 − 1 where Q n denotes the n -cube. We prove that for 4$"> n > 4 , 7 ⋅ 2 n − 4 ≤ α ( Q n ) ≤ 2 n − 1 − 2 n − y − 2 , where y = [ log 2 ( n − 1 ) ] . We show that the upper bound is obtained for n ≤ 8 and conjecture that it is obtained for all n .