Step 1: Understanding the Concept:
In Bronsted-Lowry theory a base accepts a proton. Every acid has a conjugate base. The weaker the acid, the stronger its conjugate base.
Step 2: Key Approach:
Write the parent acid of each ion, then compare acid strengths. The ion whose parent acid is weakest is the strongest base.
Step 3: Parent acids:
\(Cl^-\) comes from HCl, a very strong acid. \(NO_3^-\) comes from \(HNO_3\), a very strong acid. \(HSO_4^-\) comes from \(H_2SO_4\), a strong acid. \(CH_3COO^-\) comes from \(CH_3COOH\), a weak acid with \(K_a \approx 1.8\times 10^{-5}\).
Step 4: Decide:
Only acetic acid is weak. So its conjugate base, acetate ion, holds on to a proton most strongly. The other three ions are very poor proton acceptors. So acetate is the strongest base, option (B).
Final Answer:
Acetate is the conjugate base of the only weak acid in the list.
\[ \boxed{B:\ \text{CH}_3\text{COO}^-} \]