When Stalin died in 1953, many in the West, including Eisenhower, understood that there was a window of opportunity to strike a different tone with the new Soviet leadership. After some internal struggle, Nikita Khrushchev ended up as Premier, and he actually did have a very different governing philosophy from his genocidal predecessor.

Ike gave this speech to the American Society of Newspaper Editors fully expecting its text to be pored over by Soviet analysts for any clues as to what the great Capitalistic Scourge was planning next. And so it's ridiculously clear: The U.S. and the West want peace with the Soviet Union. All the U.S.S.R. has to do is make consistent peaceful gestures, and the Cold War can start to wind down.

Ike's granddaughter Susan, no slouch herself in the fields of international relations and political analysis, saw the "Chance for Peace" speech and the Farewell Address as "bookends" of Ike's presidency. She thought that some people saw the Farewell Address as an afterthought, when in fact, the concerns he expressed in it had been there since before he took office. For example:

This world in arms is not spending money alone. It is spending the sweat of its laborers, the genius of its scientists, the hopes of its children. The cost of one modern heavy bomber is this: a modern brick school in more than 30 cities. It is two electric power plants, each serving a town of 60,000 population. […] We pay for a single fighter with a half-million bushels of wheat. We pay for a single destroyer with new homes that could have housed more than 8,000 people. […] This is not a way of life at all, in any true sense. Under the cloud of threatening war, it is humanity hanging from a cross of iron. (Source)

Susan knew that her generation was a beneficiary of Ike's focus on the future. Just like his "Farewell Address," Ike's "Chance for Peace" Speech was a warning that only focusing on the enemy outside could destroy the nation from the inside.