To arrange the given historical events in chronological order, we must understand when each event occurred and list them from earliest to latest.

1. Cuban Missile Crisis (E): This event occurred in October 1962. It was a pivotal moment in the Cold War between the United States and the Soviet Union, involving the deployment of nuclear missiles in Cuba.
2. Apollo I Tragedy (D): On January 27, 1967, a cabin fire during a launch rehearsal test killed all three crew members on board the Apollo 1 spacecraft, marking a tragic moment in NASA’s space exploration history.
3. Cambodian Genocide under Pol Pot (C): This occurred roughly from 1975 to 1979 when the Khmer Rouge, led by Pol Pot, initiated a brutal regime in Cambodia, resulting in the deaths of millions.
4. Chernobyl Disaster (B): On April 26, 1986, the Chernobyl nuclear power plant in Ukraine experienced a catastrophic nuclear accident, leading to widespread radioactive contamination.
5. Tiananmen Square Massacre (A): Taking place on June 4, 1989, this was a tragic incident where the Chinese military forcefully suppressed pro-democracy protesters in Beijing's Tiananmen Square.

Based on the chronological order of events from earliest to latest, the correct arrangement is:

The option "E, D, C, B, A" is correct because it follows the chronological timeline from the 1962 Cuban Missile Crisis to the 1989 Tiananmen Square Massacre. Therefore, option B is the correct answer.