Of the given anions, the strongest Bronsted base is

The acidic strength of chlorate acids are as follows:

${\text{HClO}}_{\text{4}}{\text{HClO}}_{\text{3}}{\text{HClO}}_{\text{2}}\text{HClO}$

The corresponding strength of their conjugate $\text{bases are } \text{ Cl}{{\text{O}}_{\text{4}}}^{\text{-}}\text{,Cl}{{\text{O}}_{\text{3}}}^{\text{-}}\text{,Cl}{{\text{O}}_{\text{2}}}^{\text{-}}{\text{,ClO}}^{\text{-}}$

When the acid is strong, the corresponding conjugate base will be weak because the ensuing conjugate base becomes more stable and does not react when acids give up their protons.

Following is the order of the conjugate bases' basic strengths:

$\text{Cl}{{\text{O}}_{\text{4}}}^{\text{-}}\text{ Cl}{{\text{O}}_{\text{3}}}^{\text{-}}\text{ Cl}{{\text{O}}_{\text{2}}}^{\text{-}}{\text{ ClO}}^{\text{-}}$

The strongest base will be ${\text{ClO}}^{-}$.

Hence, the correct option is option (A) ${\text{ClO}}^{-}$.