To boldly go ...where no writer has been before

Is it possible to write an original story? 

Yes.
There are many story patterns and similar themes - murder mystery, romance, fighting aliens, fulfilling a prophecy, saving the world ... and they can be told in a multitude of different ways.
Every cliche can be twisted.
Every scene can have an unexpected turn, maybe the opposite to what you were going to write - but the opposite works and is an original choice.
Original use of a tool or animal, NB: If you have giant wolves rather than horses, but they fulfil a horses role why have wolves? What do they do to push the plot forward that a horse couldn't.

But
Originality is not necessarily your characters, plot, or genre. 
It is you. Understand where your ideas and writing passion is coming from.
Write with passion and experience the freshness of your story and the reader will too.
The reader is experiencing the world through your eyes, experience, thoughts, emotions and imagination. That is what makes a story unique.

Be brave.
Do not be a safe writer, following guidelines or trends.
Boldly go where only you have travelled.
Write freely for the first draft, let anything happen, go with your imaginative flow, write the same scene twice in different ways, experiment,, write out of sequence.

Be specific.
You want the reader to see your character and world the way you do? Describe them carefully, pick the perfect words. Not on the first draft, but when you are editing. 


Set your Phasers and stun your readers!