Tested and worked in IE, Firefox, Chrome, Safari and Opera. I did not test IE6. The outer text-align is needed for IE. Other browsers (and IE9?) will work when you give the DIV margin (left and right) value of auto. Margin "0 auto" is a shorthand for margin "0 auto 0 auto" (top right bottom left).
Note: the text is also centered inside the inner DIV, if you want it to remain on the left side just specify text-align: left; for the inner DIV.
Edit: IE 6, 7, 8 and 9 running on the Standards Mode will work with margins set to auto.
