Thank you Perú, you were magnificent.
I arrived in Chile after flying from Arequipa to Tacna near the border. The crossing was made simple by taking a taxi from Tacna in Perú to Arica which is just across the border. The taxi driver does all the paperwork. The whole process takes about an hour and a half, which includes the travelling time, and costs US$55.
I have had a comfortable 2 nights in a hotel and tonight I will be travelling by bus to San Pedro de Atacama. It will be an 11 hour bus ride after which I intend to spend a few days exploring the desert.