The chlorine atom of the following compound

that reacts most readily with ${\mathrm{AgNO}}_3$ to give a precipitate is

The reaction between haloalkane and $\mathrm{AgNO}$ gives carbocation intermediate. So, more easily it will be formed, more readily it will react to give precipitate.
In the given compound

${\mathrm{Cl}}^{\mathrm{a}}$ is easily lost from this compound and carbocation formation takes place readily. This is because this ${\mathrm{Cl}}^{\mathrm{a}}$ is closest to electronegative atom $0,$ which will attract the electron density towards itself and readily leaves $\mathrm{C}-{\mathrm{Cl}}^{\mathrm{a}}$bond. Hence, it will most readily react with  ${\mathrm{AgNO}}_3$ to give precipitate.