In this work, a high temperature (HT) homogeneous charge compression ignition (HCCI) critical compression ratio (cCR) was defined as the compression ratio which resulted in HCCI combustion with a crank angle location of 50% fuel burned (CA50) of 3.0 degrees after top dead center (aTDC) while operating at an equivalence ratio of 0.33 (λ = 3), an intake pressure of 1.0 bar (naturally aspirated), an intake temperature of 473 K (200°C), and an engine speed of 600 rpm. Using a Cooperative Fuel Research engine, the HT HCCI cCR of seven alcohol fuels were experimentally determined and found to be ordered as follows (ordered from least reactive to most reactive): isopropanol > sec-butanol > methanol ≈ ethanol ≈ n-propanol ≈ isobutanol > n-butanol. The HT HCCI cCR for the alcohol fuels correlated well with experimental HCCI data from a modern gasoline direct injection (GDI) engine architecture with a pent-roof head and a rebreathe valvetrain. The HT HCCI cCR was also correlated with available cetane number (CN), motor octane number (MON), and research octane number (RON) values found in the literature. The coefficient of determination (R2) for these correlations was 0.02, 0.95, and 0.69, respectively. When the RON values were modified to account for the high cooling potential of the alcohol fuels, the R2 increased from 0.69 to 0.96. When a wider array of other fuels were considered, including pure components of different fuel classes, pure-component fuel blends, and gasoline fuel blends, the critical compression ratio no longer correlated well with MON or HOV-modified RON. It was concluded that when fuels of a similar fuel class are considered, such as neat C1-C4 alcohols, MON or an HOV-modified RON may be sufficient to compare the HCCI reactivity of the fuels at MON-like cylinder conditions. However, due to the complex nature of the octane number tests, the HCCI ignition propensity is not well predicted by the standard octane numbers when fuels of varying chemical characteristics and combustion chemistry attributes are considered. Therefore, a metric for characterizing gasoline-like fuels under compression ignition conditions is required, such as an HCCI test method on the CFR octane rating engine.