  We construct dark energy stars with Chaplygin-type equation of state (EoS) in
the presence of anisotropic pressure within the framework of Einstein gravity.
From the classification established by Iyer et al. [Class. Quantum Grav. 2, 219
(1985)], we discuss the possible existence of isotropic dark energy stars as
compact objects. However, there is the possibility of constructing
ultra-compact stars for sufficiently large anisotropies. We investigate the
stellar stability against radial oscillations, and we also determine the moment
of inertia and tidal deformability of these stars. We find that the usual
static criterion for radial stability $dM/d\rho_c >0$ still holds for dark
energy stars since the squared frequency of the fundamental pulsation mode
vanishes at the critical central density corresponding to the maximum-mass
configuration. The dependence of the tidal Love number on the anisotropy
parameter $\alpha$ is also examined. We show that the surface gravitational
redshift, moment of inertia and dimensionless tidal deformability undergo
significant changes due to anisotropic pressure, primarily in the high-mass
region. Furthermore, in light of the detection of gravitational waves GW190814,
we explore the possibility of describing the secondary component of such event
as a stable dark energy star in the presence of anisotropy.
