$$Cl_2 + H_2O \longrightarrow HCl + HClO_3$$

To balance the equation, we need to make sure that the number of atoms of each element is the same on both sides of the equation.

We start by balancing the chlorine atoms. We have two chlorine atoms on the left side of the equation, and one chlorine atom on the right side. To balance this, we need to add a coefficient of 2 to HCl. This gives us:

$$Cl_2 + H_2O \longrightarrow 2HCl + HClO_3$$

Now, we need to balance the hydrogen atoms. We have two hydrogen atoms on the left side of the equation, and four hydrogen atoms on the right side. To balance this, we need to add a coefficient of 2 to H2O. This gives us:

$$Cl_2 + 2H_2O \longrightarrow 2HCl + HClO_3$$

Finally, we need to balance the oxygen atoms. We have two oxygen atoms on the left side of the equation, and three oxygen atoms on the right side. To balance this, we need to add a coefficient of 2 to HClO3. This gives us:

$$Cl_2 + 2H_2O \longrightarrow 2HCl + 2HClO_3$$

The equation is now balanced.