Step 1: Oxidation state of chromium.
Benzene and the three carbonyls are all neutral, so chromium is in the zero state.
Step 2: Electron count and field.
This is an 18 electron complex and carbon monoxide is a strong field ligand, so all electrons pair up.
Step 3: Unpaired electrons.
With everything paired the count of unpaired electrons is zero.
Step 4: Answer.
\[ \boxed{0} \]