By utilizing the styles below:
.divideMe{
width:100px;
word-wrap: break-word;
}
<div class='divideMe'>reallyreallyreallyreallyreallyreallylongstring</div>
The result would be:
reallyreallyreally
reallyreallyreallyl
ongstring
While this method doesn't break the word into chunks, you can still easily select it by double or triple clicking. This property is based on CSS3 and appears to function well across various browsers I have tested. Note that browser compatibility may vary.
It has been tested and works smoothly on IE 6,7,8 as well as FF 3.6
An alternative solution could involve hiding the overflow and displaying a scroll bar if you prefer to keep the text in one line. However, since the initial objective was to display the entire string without concealment, this approach may be preferable.