  In this letter, we investigate the impact of environment on integrated and
spatially-resolved stellar kinematics of a sample of massive, quiescent
galaxies at intermediate redshift ($0.6<z<1.0$). For this analysis, we combine
photometric and spectroscopic parameters from the UltraVISTA and Large Early
Galaxy Astrophysics Census (LEGA-C) surveys in the COSMOS field and
environmental measurements. We analyze the trends with overdensity (1+$\delta$)
on the rotational support of quiescent galaxies and find no universal trends at
either fixed mass or fixed stellar velocity dispersion. This is consistent with
previous studies of the local Universe; rotational support of massive galaxies
depends primarily on stellar mass. We highlight two populations of massive
galaxies ($\log M_\star/M_\odot\geq11$) that deviate from the average mass
relation. First, the most massive galaxies in the most under-dense regions
($(1+\delta)\leq1$) exhibit elevated rotational support. Similarly, at the
highest masses ($\log M_\star/M_\odot\geq11.25$) the range in rotational
support is significant in all but the densest regions. This corresponds to an
increasing slow-rotator fraction such that only galaxies in the densest
environments ($(1+\delta)\geq3.5$) are primarily (90$\pm$10\%)
slow-rotators.This effect is not seen at fixed velocity dispersion, suggesting
minor merging as the driving mechanism: only in the densest regions have the
most massive galaxies experienced significant minor merging, building stellar
mass and diminishing rotation without significantly affecting the central
stellar velocity dispersion. In the local Universe, most massive galaxies are
slow-rotators, regardless of environment, suggesting minor merging occurs at
later cosmic times $(z\lesssim0.6)$ in all but the most dense environments.
