It is no surprise that grapes and olives grow side by side. And great olive oil is like great wine - the soil, the climate, and human care makes it world class.
There are many great oil regions in Portugal. The Portuguese take their olive oil, called azeite, very seriously.
Like the grape vine and cork trees, the olive tree has been a part of the Portuguese landscape since ancient times. The quality of the soil and the climate (which varies on a Peninsula) dictate the quality and diversity of the olive oils produced. So never eat an olive off a tree - it could break a tooth. Brine makes them so tasty. And check out the fall olive harvest - still done in the traditional way. And the wonderful Moura Olive Museum: http://en.lifecooler.com/lifecooleren/olive-oil-museum-varas-de-fojo-olive-press-museums-385913-1.html
Portugal has six "DOC" regions with Protected Designation of Origin for olive oil: Trás-os-Montes, Beira Interior, Ribatejo, Moura, Alentejo Interior and Norte Alentejano. Needless to say, those are some good olives!