Step 1: Identify the parent chain.
The parent chain is benzene.
Step 2: Number the benzene ring to give the lowest locants to the substituents, prioritizing alphabetical order.
Substituents are chloro (-Cl), methyl (-CH$_3$), and nitro (-NO$_2$). Alphabetical order: chloro, methyl, nitro.
Assign position 1 to the carbon with chloro. Numbering clockwise gives methyl at 2 and nitro at 4 (1, 2, 4). Numbering counterclockwise gives methyl at 6 and nitro at 3 (1, 3, 6). The lowest set is 1, 2, 4.
Step 3: Name the substituents with their positions.
Chloro at position 2
Methyl at position 1
Nitro at position 4
Step 4: Write the IUPAC name in alphabetical order of substituents followed by benzene.
2-chloro-1-methyl-4-nitrobenzene
Thus, the IUPAC name is $ \boxed{2 - Chloro - 1 methyl - 4 - nitrobenzene} $.