01:02:03 04/05/06
Issue 38; 05 Apr 2006; last modified 08 Oct 2010
, Not palindromic, but fun.
At two minutes and three seconds after one o'clock this morning, it was 01:02:03 04/05/06. If you follow the European convention of DD/MM/YY instead of the American convention of MM/DD/YY, you get your chance on the fourth of May.
Thanks to Henry for pointing it out to me.