I just decided to transfer a Youtuber's rendition of this song onto a more easily 
readable format. I don't take credit for this. 
Original video's URL: http://www.youtube.com/watch?v=tKBi35gBXyc

Bb (x1333x@1)     C (x32010@1)    Am (x02210@1)  Dm (xx0231@1)name="chord_x1333x@1">Bb  CTo (x32010@1)to ro totoro to to ro totoro.........

F (133211@1)    C (x32010@1)Dm (xx0231@1)name="chord_x02210@1">Am
Dareka ga kossori
Bb (x1333x@1)       Gm (355333@1)     C (x32010@1) 
Komichi ni ko no mi uzumete
F (133211@1)      C (x32010@1)Dm (xx0231@1)name="chord_x02210@1">Am
Chiisana me haetara 
Bb (x1333x@1)         Bbmhimitsu (x13321@1)no ango
       F (133211@1)      D7Mori (xx0212@1)e no pasupooto
Bb (x1333x@1)     Gm (355333@1)          CSutekina (x32010@1)bouken hajimaru

Chorus:

F (133211@1)        C (x32010@1)        A7 (x02020@1) DmTonari (xx0231@1)no to to ro totoro to to ro totoro
Bb (x1333x@1)      F (133211@1)   Gm (355333@1)         CMori (x32010@1)no naka ni mukashi kara sunderu
          F (133211@1)        C (x32010@1)        A7 (x02020@1) DmTonari (xx0231@1)no to to ro totoro to to ro totoro
Bb (x1333x@1)C (x32010@1)        Am (x02210@1)name="chord_xx0231@1">Dm   Bb (x1333x@1)          C (x32010@1)      
Kodomo no toki ni dake anata ni otozureru
             F (133211@1)   BbFushigina (x1333x@1)deai

F (133211@1)   C (x32010@1) Dm (xx0231@1) AmAme (x02210@1)furi basu tei
Bb (x1333x@1)     Gm (355333@1)     C (x32010@1) 
Zubunure obake ga itara
F (133211@1)   C (x32010@1)Dm (xx0231@1)  Am (x02210@1)Anata no amagasa 
Bb (x1333x@1)          Bbmsashite (x13321@1)agemasho
        F (133211@1)     D7Mori (xx0212@1)e no pasupooto
Bb (x1333x@1)     Gm (355333@1)         CMahou (x32010@1)no tobira akimasu

F (133211@1)        C (x32010@1)     A7 (x02020@1)    DmTonari (xx0231@1)no to to ro totoro to to ro totoro
Bb (x1333x@1)    F (133211@1)    Dm (xx0231@1)name="chord_355333@1">Gm         CTsukiyo (x32010@1)no ban ni okarina fuiteru
          F (133211@1)        C (x32010@1)     A7 (x02020@1)    DmTonari (xx0231@1)no to to ro totoro to to ro totoro
Bb (x1333x@1) C (x32010@1)  Am (x02210@1) Dm (xx0231@1) Bb (x1333x@1)            CMoshimo (x32010@1)aeta nara sutekina shiawase ga
         F (133211@1)    
Anata ni kuru wa

Bb C F