  We present results from the first recorded stellar occultation by the large
trans-Neptunian object (174567) Varda that was observed on September 10$^{\rm
th}$, 2018. Varda belongs to the high-inclination dynamically excited
population, and has a satellite, Ilmar\"e, which is half the size of Varda. We
determine the size and albedo of Varda and constrain its 3D shape and density.
Thirteen different sites in the USA monitored the event, five of which detected
an occultation by the main body. A best-fitting ellipse to the occultation
chords provides the instantaneous limb of the body, from which the geometric
albedo is computed. The size and shape of Varda are evaluated, and its bulk
density is constrained, using Varda's mass known from previous works. The
best-fitting elliptical limb has semi-major (equatorial) axis of $(383 \pm
3)$km and an apparent oblateness $0.066\pm0.047$ corresponding to an apparent
area-equivalent radius $R'_{\rm equiv}= (370\pm7)$km and geometric albedo
$p_v=0.099\pm 0.002 $ assuming a visual absolute magnitude $H_V=3.81\pm0.01$.
Using three possible rotational periods for the body (4.76h, 5.91h, and 7.87h),
we derive corresponding MacLaurin solutions. Furthermore, given the
low-amplitude ($0.06\pm0.01$) mag of the single-peaked rotational light-curve
for the aforementioned periods, we consider the double periods. For the 5.91h
period (the most probable) and its double (11.82h), we find bulk densities and
true oblateness of $\rho=(1.78\pm0.06)$ g cm$^{-3}$, $\epsilon=0.235\pm0.050$
and $\rho=(1.23\pm0.04)$ g cm$^{-3}$, $\epsilon=0.080\pm0.049$. However, it
must be noted that the other solutions cannot be excluded just yet.
