The peaceful, side-by-side rise of China and India has been taken for granted in many quarters. But tensions between the two giants are mounting, and Washington would do well to take note. On June 8, New Delhi announced it would deploy two additional army divisions and two air force squadrons near its border with China. Beijing responded furiously to the Indian announcement, hardening its claim to some 90,000 square kilometers of Indian territory that China disputes.

To understand what the tussle is about, consider recent history: The defining moment in the Sino-Indian relationship is a short but traumatic war fought over the Sino-Indian border in 1962. The details of that conflict are in dispute, but the outcome is not: After a sweeping advance into Indian territory, China...