Like most of The Terror, this song is built off of just a few chords. 
Intro (0:00-0:24) 
     Dm 
verse 1 (0:24-1:59) 
     Dm 
     Always there, in our hearts, 
     Fear of violence and of death 
     Always there, in our hearts, 
     There is love and there is pain 
     Always there, in our hearts, 
     There is evil that wants out 
     Always there, in our hearts, 
     There are sorrows and sadness 
     Always there, in our hearts, 
     Never understanding 
     Always there, in our hearts, 
     Something pure that we can't control 
     Can't control, can't control, can't control 
To play the scratchy guitar part that starts around 1:50, 
just play this chord over and over: 
E|-10-| 
B|-10-| 
G|-10-| 
D|-12-| 
A|----| 
E|----| 
Unsurprisingly, this chord is also D minor. 
Bridge (1:59-2:40) 
     F   Dm   C   Dm   Dm   Dm   Dm   Dm 
                       **drums start here 
     F   Dm   C   Dm   Dm   Dm   Dm   Dm 
https://www.coveralia.com/acordes/always-there--in-our-hearts-the-flaming-lips.php
      
      
     Dm   Dm   Dm   Dm   F   Dm   C   Dm 
      
      
     Dm   Dm    
verse 2 (2:40-3:49) 
     Dm 
     Always there, in our hearts, 
     Dm 
     Destroying everything we know 
     Dm 
     Always there, in our hearts, 
     F      Dm           C       Dm 
     Not forgiving those who are weak 
     Dm 
     Always there, in our hearts, 
     F      Dm           C      Dm 
     Shame that we are all powerless 
     Dm 
     Always there, in our hearts, 
     F      Dm         C   Dm 
     Joy of life that overwhelms  
     Dm        
     Overwhelms, overwhelms, 
     F   Dm      C   Dm 
     Overwhelms, overwhelms, 
     Dm         Dm 
     Overwhelms 
Outro (3:49-4:35) 
     F   Dm   C   Dm   F   Dm   C   Dm 
     F   Dm   C   Dm    
     Dm