Natural β-cyclodextrin (cyclomaltoheptaose) was treated with sodium hydride and allyl bromide to form the per- O-allyl-β-cyclodextrin. 9-BBN, sodium hydroxide and hydrogen peroxide were then added to form, after adequate treatments, the desired per- O-(3-hydroxy)propyl-β-cyclodextrin in yields close to 65%. This modified cyclodextrin, which bears only primary hydroxyl groups, can be used as a macro-initiator of the anionic polymerisation of ethylene oxide to form star-shaped polymers. The presence of only primary hydroxyl groups allows us to expect identical initiation kinetics for all the hydroxyl groups of the modified glucopyranosyl units.