Hydroperoxyalkylperoxy (OOQOOH) radical isomerization is an important low-temperature chain branching reaction within the mechanism of hydrocarbon oxidation. This isomerization may proceed via the migration of the α-hydrogen to the hydroperoxide group. In this work, a combination of high level composite methods - CBS-QB3, G3 and G4 - is used to determine the high-pressure-limit rate parameters for the title reaction. Rate rules for H-migration reactions proceeding through 5-, 6-, 7- and 8-membered ring transitions states are determined. Migrations from primary, secondary and tertiary carbon sites to the peroxy group are considered. Chirality is also investigated by considering two diastereomers for reactants and transition states with two chiral centers. This is important since chirality may influence the energy barrier of the reaction as well as the rotational energy barriers of hindered rotors in chemical species and transition states. The effect of chirality and hydrogen bonding interactions in the investigated energies and rate constants is studied. The results show that while the energy difference between two diastereomers ranges from 0.1 - 3.2 kcal, chirality hardly affects the kinetics, except at low temperatures (atmospheric conditions) or when two chiral centers are present in the reactant. Regarding the effects of the peroxy group position and the H-migration ring size, it is found that in most cases, the 1,5 and 1,6 H-migration reactions have similar rates at low temperatures (below ~830K) since the 1,6 H-migration proceeds via a cyclohexane-like transition state similar to that of the 1,5 H-migration.