We present the high-resolution X-ray spectrum of the low-redshift quasar H1821+643 and its surrounding hot cluster observed with the Chandra High-Energy Transmission Grating Spectrometer. An iron emission line attributed to the quasar at similar to6.43 keV (rest frame) is clearly resolved, with an equivalent width of similar to100 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 emission feature at similar to6.9 keV (rest frame). We suggest that both lines could originate in an accretion disk composed 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 (IGM) along the similar to1.5 h(-1) Gpc line of sight to the quasar. No absorption features are detected at or above the 3 sigma level, while a total of six O VI intervening absorption systems have been detected with the Hubble Space Telescope and Far Ultraviolet Spectroscopic Explorer. Based on the lack of O VII and O VIII absorption lines and by assuming collisionally ionization, we constrain the gas temperature of a typical O VI absorber to 10(5) K<T<10(6) K, which is consistent with the results from hydrodynamic simulations of the IGM. 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 similar to10 keV and a metal abundance of similar to0.3 Z(circle dot). 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.