Quasars may have played a key role in limiting the stellar mass of massive galaxies. Identifying those quasars in the process of removing star formation fuel from their hosts is an exciting ongoing challenge in extragalactic astronomy. In this paper we present X-ray observations of eleven extremely red quasars (ERQs) with $L_{rm bol}sim 10^{47}$ erg s$^{-1}$ at $z=1.5-3.2$ with evidence for high-velocity ($v > 1000$ km s$^{-1}$) [OIII]$lambda$5007AA outflows. X-rays allow us to directly probe circumnuclear obscuration and to measure the instantaneous accretion luminosity. We detect ten out of eleven extremely red quasars available in targeted and archival data. Using a combination of X-ray spectral fitting and hardness ratios, we find that all of the ERQs show signs of absorption in the X-rays with inferred column densities of $N_{rm H}approx 10^{23}$ cm$^{-2}$, including four Compton-thick candidates ($N_{rm H} > 10^{24}$ cm$^{-2}$). We stack the X-ray emission of the seven weakly detected sources, measuring an average column density of $N_{rm H}sim 8times 10^{23}$ cm$^{-2}$. The absorption-corrected (intrinsic) $2-10$ keV X-ray luminosity of the stack is $2.7times 10^{45}$ erg s$^{-1}$, consistent with X-ray luminosities of type 1 quasars of the same infrared luminosity. Thus, we find that ERQs are a highly obscured, borderline Compton-thick population, and based on optical and infrared data we suggest that these objects are partially hidden by their own equatorial outflows. However, unlike some quasars with known outflows, ERQs do not appear to be intrinsically underluminous in X-rays for their bolometric luminosity. Our observations indicate that low X-rays are not necessary to enable some types of radiatively driven winds.
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