Can one have morality without a God? Yes! (of course)
There is so much to say about this subject, but in short, atheists have proven to be more moral that religionists anywhere in the world. See the articles and studies below.
In short, no one needs a deity for be moral. Morality is innate within us as shown by recent studies with 6-8 month old babies.
Matt Dillahunty: The Superiority of Secular Morality (video)
3/6/14 James Kirk Wall replies to Mark Thompson’s claim of Christian moral supremacy
Ben Bova’s article HERE
In Atheists We Distrust
Ask the Atheist article HERE
Phil’s answer HERE
From Mark Vuletic HERE
From a mistaken Pastor: There are no good atheists (make sure and see the comment section)
Where does morality come from if not through a supernatural law-giver?
See the video HERE of proof that animals have morality
Read the study which shows that 6-month olds have morality