Automatically capitalize first letter of first word in a new sentence in LaTeX

I know one of LaTeX's bragging points is that it doesn't have this Microsoftish behavior. Nevertheless, it's sometimes useful.

LaTeX already adds an extra space after you type a (non-backslashed) period, so it should be possible to make it automatically capitalize the following letter as well.

Is there an obvious way to write a macro that does this, or is there a LaTeX package that does it already?