Step 1: The largest chord of a circle is its diameter. The diameter of a circle is given by:
\[
\text{Diameter} = 2 \times \text{Radius}.
\]
Step 2: Substituting the given radius \( 3 \, \text{cm} \), we find:
\[
\text{Diameter} = 2 \times 3 = 6 \, \text{cm}.
\]
Hence, the largest chord is \( 6 \, \text{cm} \).