Well, I worked out the chords using the bass tab, so it may not be 100% right. But 
this is basically how I play it. Listen to the song to hear the strumming pattern.

Chords used in song:
Bm- x24432
D-  xx0232
A-  x02220
G-  320003

Intro- Bm

Verse 1-
D
And now it's just gone after dark
And we move to the other part of it
Bm
Secret part of your restless heart
D
To glide past every city light
Bm
Like a satellite careering through the sky
This colour, this summer night

Bridge-
D
It's your heart, it's your heart
Bm
That gives me this western feeling

Chorus -
D                     A
It's your heart, it's your heart
            G
That gives me this western feeling
D               A
Do you know, you give me
            G
You give me this western feeling

(Follow the same pattern through out the whole song)

Verse 2-
Now look back see how far you've come
Will you unravel in the sun
Come undone, find your place
Held up high said from string as well
No return to that restless place
You've reached it, you've found your grace

Bridge-
It's your heart, it's your heart
That gives me this western feeling

Chorus-
It's your heart, it's your heart
That gives me this western feeling
Oh do you know, you give me

(For this section use broken chords to give the same effect as the keyboard in the original track)
You give me this western feeling
It's your heart, it's your heart
That gives you this western feeling

(Go back to strumming for the rest of the song)
It's your heart, that gives you, 
That gives you this western feeling
It's your heart, that gives you
That gives you this western feeling

Oh how do you know, what gives me, 
What gives me this western feeling
Oh how do you know, what gives me, 
What gives me this western feeling