What is the oxidation state of an individual chlorine atom in liclo2?

In this compound: Li is +1, Cl is +3 and O is -2.

This is called lithium chlorite. The ions that are present is Li+ and ClO-2

The oxidation number of an element is the charge on the atom if and only if the compound is entirely ionic.

Oxygen has a charge of -2.

So in ClO-2, the oxygens contribute 2 x -2 = 4.

But you know that the charge on the ion is -1, then Cl must be +3. Solution:

Li+ Cl + 2O = 0 

+1 + Cl + 2(-2) = 0 

Cl = +3

So the net charge would be:+ 3 - 4 = -1. 

In Li+ the oxidation state of it must be +1 and Chlorine is +3.