Display Date of Posts Once on Loop

I maid a number of attempts searching for the answer on these forums but with no success.

Essentially, since there is a high volume of posts a day, we don’t see the need to post the date at the top of each particular post. Rather we want to group them by days. One date for all the posts that day. This should be fairly easy to do, but I am at a loss for how to do it. It would look, roughly, like this in the loop:

January 2, 2008

[post #1]
[post #2]
[post #3]

January 1, 2008

[post #4]
[post #5]
…
etc.

Any thoughts?