**Solution:**

To calculate the moles of KCl required to produce 10 moles of Cl2, we need to determine the stoichiometry of the reaction between KClO3 and Cl2. The balanced equation for the reaction is as follows:

2 KClO3 → 2 KCl + 3 O2

From the balanced equation, we can see that for every 2 moles of KClO3, we obtain 2 moles of KCl. Therefore, the molar ratio between KClO3 and KCl is 1:1.

Now, we need to find the moles of KClO3 required to produce 10 moles of Cl2. Since the molar ratio between KClO3 and Cl2 is 2:3, we can set up the following proportion:

2 moles KClO3 / 3 moles Cl2 = x moles KClO3 / 10 moles Cl2

Cross-multiplying and solving for x, we get:

x moles KClO3 = (2 moles KClO3 / 3 moles Cl2) * 10 moles Cl2

x moles KClO3 = 6.67 moles KClO3

Since the molar ratio between KClO3 and KCl is 1:1, the moles of KCl required will also be 6.67 moles.

Therefore, the moles of KCl required to produce 10 moles of Cl2 by the reaction with KClO3 is 6.67 moles.

**Summary:**

- The balanced equation for the reaction between KClO3 and Cl2 is 2 KClO3 → 2 KCl + 3 O2.
- The molar ratio between KClO3 and KCl is 1:1.
- The molar ratio between KClO3 and Cl2 is 2:3.
- To calculate the moles of KCl required to produce 10 moles of Cl2, we can set up a proportion and solve for x.
- The moles of KCl required is found to be 6.67 moles.