IsisCode gives you a good solution. Another one is to position border div inside parent div. Check this example http://jsfiddle.net/A2tu9/
UPD: You can also use pseudo element :after
(:before
), in this case HTML will not be polluted with extra markup:
.my-div {
position: relative;
padding: 4px;
...
}
.my-div:after {
content: '';
position: absolute;
top: -3px;
left: -3px;
bottom: -3px;
right: -3px;
border: 1px #888 solid;
}