Intro: 

     C       C7         Cmaj7        F                        Cm7   Dsus2/C 
|e|--------------------------------------------1p0-----0-----------------------------------------| 
|B|---1--1---1-1---1-1-1---1-1-1-1----1---1-1--1---1h3---1h3p1--1-1---1-1-1---1-1--1-1-1--1-1-1--| 
|G|---0--0---0-3---0-0-0---4-0-0-0----0h2-2-2--2----------------0-0h2 2-2-2---2-2--2-2-2--0-0-0--| 
|D|---2--2---2-2---2-2-2---2-2-2-2----3---3-3--3----------------0-0---0-0-0---0-0--0-0-0--0-0-0--| 
|A|---3--3---3-3---3-3-3---3-3-3-3------------------------------3-3---3-3-3---3-3--3-3-3--3-3-3--| 
|E|----------------------------------------------------------------------------------------------| 
     d   d   d u   u d u   d u d u   d   d u  u  *F chord*   u d   d u d   d u  u d u  u d u   
                                       ^Try playing F chord at same time^ 
 C/G 
|e|-------------------------------------------------|| 
|B|1----1-1-1---1-1---1-1-1---1-1-------------------|| 
|G|0----0-0-0---0-0---0-0-0---0-0-------------------|| 
|D|0h2--2-2-2---2-2---2-2-2---2-2-------------------|| 
|A|3----3-3-3---3-3---3-3-3---3-3-------------------|| 
|E|3----3-3-3---3-3---3-3-3---3-3-------------------|| 
  d    d u d   d u   u d u   u d  


The rest of the song is essentially: 

C -> F -> Cm7 -> C/G 

...Up until "I am warm enough..." @ 2:50 in the video. 

     C   G 
|e|---------------|     
|B|---1--1--1-----|     
|G|---0--0--0-----|   Am - Cm7 (Play around with that  maybe) C    
|D|---2--0--0-----|     
|A|---3--2--0h2---|    
|E|------3--3-----|