This depends on the type of "objective" you mean. If you mean the same kind of objective that the rules of mathematics are then no, we can't have "objective morals". If by "objective" you mean based on observations of the real world and how various actions effect the real world then yes, we can have moral objective. Even with this starting point you would still have to agree on some basic rules, for example it is wrong to harm people, before you could start exploring what objective morals would look like.

Of course, Sam Harris has covered this ground fairly well in the book "The Moral Landscape". Personally, I think that "maximizing total human happiness" is a much too difficult thing to figure out to deal with most day to day ethical and moral decisions. A very short book covering some of this ground is "A Simple Guide to Secular Morals".