Step 1: Recall Article 340 commissions.
The First Backward Classes Commission was set up in 1953 under Article 340 to investigate the conditions of socially and educationally backward classes.
Step 2: Name the chair.
It was chaired by Kaka Kalelkar (1953–55). The Commission submitted its report in 1955.
Step 3: Distinguish from later figures.
B. P. Mandal headed the Second Backward Classes Commission (1979); V. P. Singh implemented Mandal recommendations in 1990 as PM; Karpoori Thakur was a prominent OBC leader/CM but not chair of the first commission.
Step 4: Conclude.
\[
\boxed{\text{Kaka Kalelkar (Option C).}}
\]