From https://jabblog-jabblog.blogspot.com/2010/09/

"The lyrics, inspired at least by the first line of the poem, ‘The Village Blacksmith’ by Henry Wadsworth Longfellow (1807-1832) were written by J. and H. Kennedy and were set to music by Hal Kemp. The song was recorded by the Glen Miller Orchestra in 1939 with Marion Hutton. It’s delivered rather speedily and I can imagine that anyone attempting to fit in the actions would be somewhat breathless by the end!
I’ve added the ‘actions’ to the words, as clearly as I can. Remember, practice makes perfect ;-)

Underneath the spreading chestnut tree         (spread arms above head, then touch chest, head and lift arms up)
I loved him and he loved me.                                     (hands on heart, then hug)
There I used to sit upon his knee                         (hands on knees)
‘Neath the spreading chestnut tree.                   (as before)

There beneath the boughs we used to meet    (spread arms, then clasp hands)
All his kisses were so sweet;                                       (kiss fingers)
All the little birdies went ‘tweet- tweet’          (fingers make bird beaks)
‘Neath the spreading chestnut tree.                        (as before)
                                          
I said, ‘I love you and there ain’t no ifs or buts,       (hands on heart, shake finger)
He said, ‘I love you' and the blacksmith shouted, 'Chestnuts!'    (hands on heart)

Underneath the spreading chestnut tree             (as before)
There he said he’d marry me,                                        (mimic placing ring on finger)
Now you ought to see our family                               (hand indicates heights of children on ‘fa-mi-ly;)
‘Neath the spreading chestnut tree!                         (as before)"