We present the high-resolution X-ray spectrum of the low-redshift quasar H 1821+643 and its surrounding hot cluster observed with the Chandra High Energy Transmission Grating Spectrometer (HETGS). An iron emission line attributed to the quasar at ~6.43 keV (rest frame) is clearly resolved, with an equivalent width of ~100 eV. Although we cannot rule out contributions to the line from a putative torus, the diskline model provides an acceptable fit to this iron line. We also detect a weak

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... feature at ~6.9 keV (rest frame). We suggest that both lines could originate in an accretion disk comprised of a highly ionized optically thin atmosphere sitting atop a mostly neutral disk. We search for absorption features from a warm/hot component of the intergalactic medium along the ~1.5Gpc/h line of sight to the quasar. No absorption features are detected at or above the 3 sigma level while a total of six OVI intervening absorption systems have been detected with HST and FUSE. Based on the lack of OVII and OVIII absorption lines and by assuming collisionally ionization, we constrain the gas temperature of a typical OVI absorber to 10^5 < T < 10^6 K, which is consistent with the results from hydrodynamic simulations of the intergalactic medium. The zeroth order image reveals the extended emission from the surrounding cluster. We have been able to separate the moderate CCD X-ray spectrum of the surrounding cluster from the central quasar and find that this is a hot cluster with a temperature of ~10 keV and a metal abundance of ~0.3 Zo. We also independently obtain the redshift of the cluster, which is consistent with the optical results. We estimate that the cluster makes negligible contributions to the 6.9 keV iron K line flux.