Great watch by the way:

These triple calendars go for years with marginal evolutionary differences, so it can sometimes be a little difficult to age them precisely.

In this instance, though, we may have gotten a little lucky. Look at this watch that made it as "cover girl" of the 1946 brochure:

I'd say we have a match! Though there are some detail differences - the cover watch has a smaller date scale and round pushers rather than the bars of your watch.

Inside the catalogue, there is some more detail on the watch:

And here you'll see that the details are actually as per your watch; bar pushers and date scale without a line outside it.

You'll also see it was made in a number of variations including steel, gold-plated and (unusually for now, but more common at the time) both 14 and 18 carat gold versions. The 18 kt caseback in your photos suggest this is the 2558. Incidentally the (equal) most expensive watch that Heuer were selling at the time.

The 1945 catalogue explains some of the functions of a 2557 (the 14 kt version of the watch) in more detail:

So, to summarise - the watch is a 2558 triple calendar from somewhere around the mid-40s to early-50s. You can see more images of the watch and its steel counterparts here:

http://www.onthedash.com/Guide/_Chronographs/40s_50s_Triple_Calendar_Chrono/