Chain Silicates (or inosilicates) are made up of two groups: single and double chain silicates.
Single Chain Silicates are formed by sharing oxygen ion between two tetrahedra. Think of a chain of triangles joined at the points:
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In this configuration, two oxygens on each tetrahedra are shared with other tetrahedra, whilst the remaining two oxygen ions bond with other cations.
Example:
Pyroxene.

Double Chain Silicates are formed by linking one of the remaining oxygen ions with another tetrahedra. Ie, this is a process of bonding two seperate single chain silicates into a double chain silicate:
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Example:
Amphibole.

For more general information, see silicon tetrahedra.