Since Engdahl's (1983) seminar work, parasitic gaps (PGs) have been a longstanding topic of interest in syntactic theory. While PGs inside adjunct clauses have been relatively well-investigated, far less attention has been devoted to argument-internal PGs. This paper presents a novel observation about argument-internal PGs: in the double object construction, movement of the lower object cannot license a PG in the higher object, whereas a parallel configuration is possible in other ditransitive frames such as the prepositional dative construction. Examination of a wider range of data reveals that there must be a minimal structural distance (namely an intervening maximal projection) between the PG-containing XP and the licensing gap. This generalization follows from the combination of Nissenbaum's (2000) theory of PGs and an Antilocality constraint on movement: the licensing of a PG requires the movement creating the licensing gap to target a position immediately above the PG-containing XP, but this movement violates Antilocality in the double object construction. This illicit configuration can be avoided either by embedding the licensing gap or moving the PG-containing XP. The analysis has important consequences for the theory of successive-cyclic movement and the structure of ditransitives.