PURPOSE: To obtain a polymer having an especially narrow molecular weight distribution by subjecting hexamethylcyclotrisiloxane to living-anion- polymerization in the presence of a specific chelate compound in a polar solvent by using an initiator containing lithium cation.

CONSTITUTION: This polymer is obtained by subjecting hexamethylcyclotrisiloxane to anion polymerization preferably (A) by using an initiator containing a lithium cation, e.g. lithium carbanion or lithium alkoxide, (B) in the presence of a chelate compound having plural tertiary amino groups, e.g. tetramethylethylenediamine which can coordinate the lithium cation and (C) in a polar organic solvent of an ether, e.g. tetrahydrofuran. The polymerization is preferably carried out in an inert gas atmosphere or under reduced pressure at -30 to 100°C (especially 0-50°C) for 1-24hr.