Step 1: Assign charges to ligands.
- Ethylene (C$_2$H$_4$) is a neutral ligand.
- Chloride (Cl$^-$) has charge $-1$. There are 3 chlorides, so total = $-3$. Step 2: Apply oxidation number rule.
Let the oxidation number of Pt be $x$. The overall charge is $-1$.
\[
x + (0 \times 1) + (-1 \times 3) = -1
\]
\[
x - 3 = -1 \quad \Rightarrow \quad x = +2
\]
Step 3: Conclusion.
The oxidation number of Pt in [Pt(C$_2$H$_4$)Cl$_3$]$^-$ is +2.