After dealing with heelside chatter for a couple of years I got rid of it easily this year. Consider that regular or goofy, our heelsides on symmetrical boards are roughly 6 inches behind our toesides (where most of us carve like champs). Most of what's been suggested here (hands in front, reaching, etc) puts more weight on the front of the board, where we have to be to make a turn. Natural tendency from my slalom water ski days was to ride the tail out of a turn, and I had a habit of doing it on heelsides. To fix it, I just really focused on riding my forward heel hard in a heelside turn, and the chatter stopped instantly. Every time it came back- usually as I tired, I focused on my right (goofy) heel, and it cuts cleanly.
No hands needed either, but sure, reaching forward will help.