From receptors in the nose to supramolecular biopolymers, nature shows a remarkable degree of specificity in the recognition of chiral molecules, resulting in the mirror image arrangements of the two forms eliciting quite different biological responses1,2. It is thus critically important that during a chemical synthesis of chiral molecules only one of the two three-dimensional arrangements is created. Although certain classes of chiral molecules (for example secondary alcohols3,4) are now easy to make selectively in the single mirror image form, one class—those containing quaternary stereogenic centres (a carbon atom with four different non-hydrogen substituents)—remains a great challenge5-8. Here we present a general solution to this problem which takes easily obtainable secondary alcohols in their single mirror image form and in a two-step sequence converts them into tertiary alcohols (quaternary stereogenic centres). The overall process involves removing the hydrogen atom (attached to carbon) of the secondary alcohol and effectively replacing it with an alkyl, alkenyl or aryl group. Furthermore, starting from a single mirror image form of the secondary alcohol, either mirror image form of the tertiary alcohol can be made with high levels of stereocontrol. Thus, a broad range of tertiary alcohols can now be easily made by this method with very high levels of selectivity. We expect that this methodology could find widespread application, as the intermediate tertiary boronic esters can potentially be converted into a range of functional groups with retention of configuration.