Is Inositol chiral or achiral?
Having asymmetric carbon atoms does not in itself make a compound chiral.

A compound is chiral if and only if it is not super(im)posable on its mirror image.  

If there's a plane of symmetry, then reflecting in that plane gives the same thing, by definition, and that meets the criterion for super(im)posability - the mirror image is superimposable on the original and therefore the molecule is not chiral.

Only D- and L- chiro-inositol are chiral - all the other stereoisomers have planes of symmetry and are therefore not chiral.