We don’t think of painting as having begun until the Middle Ages. There isn’t much that survives from Ancient Greece and Rome, but there are some, such as the above fresco fragment showing a young woman with a turban on a balcony. The original is to be found at Malibu’s Getty Villa. She appears to be drinking something from a shallow bowl and petting a dog or cat with her left hand. While there were no oil paintings as such—not as we think of them—there were frequent wall paintings in homes, temples, and other public buildings.
If we widen our definition of painting to include mosaics, then there are some even more spectacular works such as were found at the ruins of Pompeii and Herculaneum. I have seen mosaics that have solved problems of perspective that were not seen again for over a thousand years. Take, for example, the mosaic of one of the battles of Alexander the Great below:
It has always been my belief that most people feel that the Greeks and Romans were too ancient to be bothered with, and that art really sprang into existence during the Renaissance. Not so. A visit to Italy or such excellent museums as the Getty Villa in Malibu help redress the balance. For some background, see the excellent web page on Ancient Roman Art and Art Objects. Compare this with the Bayeux Tapestry and other Medieval battle scenes, which look relatively primitive in comparison.