Saute chicken in butter until tender, about 30 minutes.
Remove to serving platter.
Add champagne to pan, scraping up bits of drippings.
Add 2/3 cup of cream and simmer over low heat until sauce is reduced by a third.
Beat remaining cream and egg yolk together.
Add a little hot champagne sauce to egg yolk; then add to saucepan, stirring constantly over low heat until slightly thickened.
Pour over chicken to serve.