Step 1: Composition rule.
The Prime Minister traditionally served as the Chairman of the Planning Commission. On its establishment (1950), Pt. Jawaharlal Nehru was PM and thus the {first Chairman}.
Step 2: Roles of others.
V. C. Mahalanobis was an eminent statistician and architect of the Second Five-Year Plan model but not Chairman; John Mathai was Finance Minister; M. Visvesvaraya advocated planning earlier but wasn’t Chair.
Step 3: Conclude.
\[
\boxed{\text{Pt. Jawaharlal Nehru (Option C).}}
\]