The course of rivers are not constant; floods and other natural events cause channels to shift over time. By 1873, the Rio Grande had moved approximately 600 acres, effectively consigning previously Mexican territory to the United States. Settlers eventually incorporated the land—known as El Chamizal—as part of El Paso. The controversy began in 1895, when Mexico claimed ownership for Mexican citizen Pedro I. García, whose title dated to 1827.

In 1910, the International Boundary Commission (later the INTERNATIONAL BOUNDARY AND WATER COMMISSION) set out to decide the matter. The following year, the tribunal recommended splitting the territory between the two nations, but the United States rejected the proposal because it did not align with prior arbitration. (According to the 1848 Treaty of Guadalupe Hidalgo and the Treaty of 1884, the border between the United States and Mexico would remain down the middle of the Rio Grande, regardless of alterations in course, as long as the movements were the result of gradual natural changes.)

In 1963, President John F. Kennedy elected to resolve the dispute largely on the terms of the 1911 proposal. Mexico accepted, and payment and land appropriation began. The American–Mexican Chamizal Convention Act of 1964 legally settled the issue. After building a man-made channel to prevent the Rio Grande from calling the boundary into question again, Presidents Lyndon B. Johnson and Gustavo Díaz Ordaz met on the border in 1967 to officially announce and celebrate the end of the dispute after more than seven decades.