Step 1: Role of Chief Election Commissioner (CEC) 
- The CEC is the head of the Election Commission of India, responsible for conducting free and fair elections. 
Step 2: Appointment process 
- According to the Constitution of India, the CEC is appointed by the \textit{President of India}. 
- The appointment is made independently and not influenced by the Council of Ministers or Parliament. 
Step 3: Why other options are incorrect 
- (A) Council of Ministers does not appoint the CEC. 
- (B) Prime Minister does not appoint the CEC directly. 
- (C) Parliament does not appoint the CEC. 
Therefore, option (D) is correct.