Many South American tsunamis have been recorded since 1562. Eight of them caused severe damage in Hawaii, Japan and the other Pacific regions. The 1960 Chilean tsunami (m=4.5) is the largest. In the present paper, the distribution of cumulative energy, the sum of tsunami mean hight squares, for each 200km segment from Colombia to Chile is investigated for the periods from 1900-1996 and 1562-1899. Distant tsunamis, such as the 1952 Kamchatka and 1964 Alaska tsunamis, arrived at this region were excluded from the analysis. For the total tsunami energy, ΣHH², during the whole period, percentages of the received energy in the 1, 000km range were 30% on the South Chilean coast, 21% on the South Peru and Central Chilean coasts and 18% on the North Chilean coast. For the recent 97-years, the arrival energy on the South Chile region is twice larger than the mean rate of energy accumulation. On the contrary, the one in 600km segment in the North Chile region, Arica to Antofagasta, is remarkably small comparing with the expecte value. On the long-term tsunami hazard, it is necessary to take precautions against the tsunami related to large earthquakes off North Chile.