No, there can never be zero opportunity cost for anything that we human beings do in this life.  In order to see why this is so, let us first look at the definition of opportunity cost.

Our opportunity cost when we choose a given action is the value of the next best thing that we could have done.  Whenever we choose one action, we must by definition choose not to do some other action.  The value of the action that we forewent is our opportunity cost. 

Every time we choose to do one thing, we are choosing not to do something else with the time and resources that we use.  If I choose to rent a movie online, I am spending the money to rent the movie and I am spending the time to watch it.  I could have used that money to buy something else.  I could have used the time to do something else.  Therefore, my choice had an opportunity cost.

There will be times when our opportunity cost cannot really be expressed in terms of money, but the cost is still there.  If I choose to stay at work and make more money instead of going to my daughter’s basketball game, I do not incur a financial opportunity cost.  However, I do incur the emotional cost of having to miss watching her play.

So long as we humans have finite lifetimes, we cannot do everything we want to do.  We always have to choose what to do.  Therefore, there is always an opportunity cost for every choice we make.