Just finished a few days of Miluim (reserve duty): naturally, this post is about chess in the IDF.
In fact, as Zvi Bar-Shira told me and is easily checked, there had been surprisingly strong chess tournaments in the IDF -- starting in the 1951 IDF championship (Hebrew). For many more easily-accessible (Hebrew-language) links for information on IDF championships, based on Tel Aviv University's Jewish Press Archives, one can go here (Hebrew link) or search the archives oneself. Many strong players had their start there.
One of the sad effects of Israel's well-known security problems is that there are quite a few chess tournaments and clubs to commemorate chess players who fell in battle. Here is one example, the circular establishing a memorial tournament in the memory of 2nd Lt. Dov Porat (no relation to the Israeli IM Porat), from Bar-Shira's archives:
Of course, chess and war go together, so it's not surprising some people will have an IDF chess set -- in sterling silver, no less -- sold to, I presume, tourists (no Israeli would be caught dead playing on an IDF set; they have quite enough of the IDF in real life, thankyouverymuch):
This set is offered by a company called Israeli Military Products (which doesn't actually have any relation to the IDF) and claims it's a "surplus" store. That's funny, I don't remember such a chess set being available at the quartermaster's store whenever I'm on reserve duty...