I wrote down the tune from Kevin Burke's performance on YouTube. Most measures have three beats and the first two go with a chord while the third does not.   Therefore, your accompaniment needs to die away or otherwise accommodate that third beat. Here are the chords for the key of C.

See where there are two C's at the end of each line? The melody notes are tied so that they are five counts long.

pick up note/G/G/G/G/G/Am/C/C for two beats
pick up note/G/G/G/G/G/Am/C/C for two beats
pick up note G/G/Am/G/G/Am/C/C for two beats
pick up note G/G/G/G/G/Am/C/C for two beats