Astronomy is the first science, it dates back to ancient times. The Greeks, Romans and Egyptians all used the stars and believed they were related to their respective gods and spirits. Today we have constellations that were named in those times that were reflective of the beliefs then. The earliest calendars were based on the movement of stars, the sun and the moon.
Some of man's first drawings, found in caves, were of heavenly bodies. Since time began, man has had an interest in the sky and the movements of the stars. Drawings of the solar system, the planet placements, was found to have been done about 300 B.C. Man also created Stonehenge to gauge the timing of the seasons.
I believe that Chemistry and Biology were the first one that were introduced to us. I think that if you look at it the science of life could have been the first discovered because shortly after people were added they started getting ill and had to figure out what was wrong which is where Biology and Chemistry started.
We have evidence that ancient civilizations were formalizing their views of the stars into what could be considered the very roots of astronomy. However, this does not make astronomy the "first science". Even before the formation of civilization, humans were practicing very basic biology experiments. All farming has biology at its heart. As people were selecting for better crops (even without understanding the processes behind it), they were practicing the first science.
I do not think that Astronomy was the first science. I think that while looking up to the stars was something mankind did in the earliest stages of our existence, I think there other cases where we used science earlier. I think those who made fire to keep warm were exhibiting a form of science.