Step-by-step transformation:
1. Oxidation (CrO\(_3\)/H\(_2\)SO\(_4\)) converts the primary alcohol to a carboxylic acid:
\[
\text{CH}_2\text{OH} \rightarrow \text{COOH}
\]
2. Chlorination using Cl\(_2\)/red P results in substitution at the α-carbon (adjacent to -COOH), forming:
\[
\text{Cl-CH}_2\text{-CH}_2\text{-COOH}
\]
Hence, the major product is: α-chloro propionic acid derivative with a correct carbon skeleton as per the original straight chain.