Simple Text Records

This is simple, I just don't know how....

I have a timer in VB6 that runs every 30 seconds.  When it runs, I want a record added to a text file with the date/time stamp.  The way I have it now, it overwrites the previous text file with the new time, instead of keeping what is there, then adding a new line in the text file for the new timestamp.

Here is what I have:

******* Start Code *****
Sub Timer1_Timer()
        Open "C:\test\stamp.txt" For Output Access Write As #3
        Print #3, Date & " " & Time
        Close #3
End Sub
***** End Code *******


I don't want to read in from the text file each time, I just want to add a new line (with line feed?) with the new date and time.   The idea is to keep a list of everytime the timer fires.

Thanks as always for any light you can shed on this incredibly problem.  :-)