Step 1: Identify the outlier whose toxicity does not involve the liver. Three options have a known hepatotoxic reputation.
Step 2: Halothane is famous for immune mediated halothane hepatitis. Chlorpropamide, an older sulfonylurea, can trigger cholestatic liver injury, and allopurinol can cause a severe hypersensitivity reaction that includes hepatitis.
Step 3: Streptomycin sits in a different toxicity bracket. As an aminoglycoside, its hallmark adverse effects are damage to the inner ear and to the kidneys.
Step 4: Since the liver is not the target organ for streptomycin toxicity, it is the drug that is not hepatotoxic.
\[\boxed{\text{Streptomycin}}\]