Step 1: Understand the question.
We must find who first used the term Public Interest Litigation (PIL). Notice the question is about the words of the term, not who built the PIL movement in India.
Step 2: Recall the Indian side.
Justice P.N. Bhagwati and Justice V.R. Krishna Iyer are the great builders of PIL in India. They opened the courts to the poor and marginalised. But they are linked to spreading PIL, not to first coining the phrase.
Step 3: Recall the origin of the term.
The actual phrase Public Interest Litigation comes from American legal scholarship. Professor Abram Chayes used and named it in his well-known 1976 article on the role of the judge in public law litigation.
Step 4: Separate the two ideas.
So we keep two things apart. The Indian judges are the architects of the movement, while the naming itself is credited to Chayes. The question asks who first used the term, so we choose Chayes.
Step 5: Reject the other options.
Bhagwati and Krishna Iyer are about the Indian movement. Upendra Baxi is a noted scholar but is not credited with first coining the term.
Step 6: State the answer.
The term was first used by Prof. Abram Chayes.
\[ \boxed{\text{Prof. Abram Chayes}} \]