Here are the chords I use.  You can get by with just G, C, D7, and Em (using C instead of Am7) if you insist that "less is more."  You can, I'm sure, add some fancier chords, too, if you're into jazz.

Genie

 Look To The Rainbow
 From "Finian's Rainbow" ca. 1947
 Lyrics: E. Y. Harburg:  Music: Burton Lane

              G            Em                 G            Em
 On the day I was born, said me father, said he,
               G        (G7)    C            (D7)
"I've an elegant legacy waiting for ye.
            D                 D7
'tis a rhyme for your lips
             Am7*            D7
 And a song for your heart
       Am7           D7                C            G
 To sing it whenever the world falls apart.

 Chorus:
 G       Em     D     D7       G
Look, look , look to the rainbow.
 Em          G           C   (Am7)   D7 
 Follow it over the hill and the stream.
 G       Em     D     D7       G
 Look, look , look to the rainbow.
 C            G              D7           G
 Follow a fellow who follows a dream.
 C             G        D    D7  G
 Follow a fellow, follow a fellow,
  C           G              D7         G
Follow a fellow who follows a dream.

              G            Em            G              Em
 'Twas a sumptuos gift to bequeath to a child,
                G             (G7)                C              (D7)
 And the lure of that song kept me feet running wild,
                D               D7                Am7*          D7
 For you'll never grow old and you'll never stand still,
              Am7                  D7              C                  G
 With the whip-poor-will's song just beyond the next hill.

  Chorus

        G                Em             G                       Em
 So I bundled my heart and I roamed the world free,
            G                (G7)            C                 (D7)
To the east with the lark, to the west with the sea,
            D                    D7           Am7*              D7
 And I searched all the hills and I scanned all the skies
        Am7        D7            C                      G
Till I found it at last in my own true love's eyes.
 
 Chorus

*This Am7 is 002010, not 002213.  I'm not positive the one I use is called Am7.