I did this without listening to the music so I'm not entirely sure but it sounds 
right so by all means try it and tell me what you think!
I think it may be in a different key but by all means try it anyway.

No Capo

Chords Used
Am
C
G

           Am          C           Am
I've heard stories and tales about puppets and whales
    Am          C         Am  G
but never heard stories of you.
         Am        C             Am              
I've not seen you around in this quiet part of town,
       Am       C                Am G
You've shown up right out of the blue.


    Am   C    Am           C
And I've been waiting for someone
   Am         C         Am             C          Am C  
to share my adventures, you seem quite perfect to me dear,
 Am       C            Am              C          Am G 
and did I mention that you seem quite perfect to me.


        Am            C
So come running, come running,
     Am              C
come running through rivers.
     Am            C   
Come running, come running
        Am           G 
through rivers with me.
        Am            C
Oh come running, come running,
     Am              C
come running through rivers.
      Am             G            Am G      
We'll show them what living should be.


       Am         C             Am           
We're pirates at sea with our world at our feet.
Am         C             Am  G
Sailing on waves made of stars.
      Am           C                 Am             
A princess needs a friend, where the laughter won't end.
             Am          C              Am G
That's worth more than a prince who can charm.


    Am   C    Am             C           Am           C
And I've been searching for someone who makes life a story, 
    Am             C          Am  C
and you seem quite perfect to me, dear.
Am           C         Am             C         Am G
You wont be sorry but you seem quite perfect to me.


        Am            C
So come running, come running,
     Am              C
come running through rivers.
     Am            C   
Come running, come running
        Am           G 
through rivers with me.
        Am            C
Oh come running, come running,
     Am              C
come running through rivers.
      Am             G            Am G      
We'll show them what living should be.



   Am        C           Am      
If things go wrong we'll just rewrite them
 Am              C              Am            C
running, you're running, you're running with me.
       Am     C          Am        
And if demons call we'll stand and fight them.
Am              C               Am            G    
Running, you're running, you're running with me.



        Am            C
So come running, come running,
     Am              C
come running through rivers.
     Am            C   
Come running, come running
        Am           G 
through rivers with me.

        Am            C
So come running, come running,
     Am              C
come running through rivers.
     Am            C   
Come running, come running
        Am           G 
through rivers with me.

        Am            C
Oh come running, come running,
     Am              C
come running through rivers.
      Am             G            Am G      
We'll show them what living should be.


           Am          C           Am
They've heard stories and tales about puppets and whales
    Am          C               Am 
And now they'll hear stories of you.



I hope this was okay, make sure to write in the comments and rate!