grace note arpeggio tied to chord

[Jim Cline]

Hello, sorry if I missed it, but I did not find it by searching the 
archives.  I would like to have a grace note arpeggio where each note is 
tied to the chord that follows:

\grace{g16~ c~ e~}<g, c e>4
I only get the tie between the e's, not the other notes.

This is similar to a rolled chord, but I want it more articulated, hence 
the grace notes.  regards, Jim