So, having been pointed to this thread a number of times now, let me start out by saying that the OP and I have a bit of history from another forum, and I am weighing in here with due dread of causing cross-forum drama. Sorry for that.
Dates for these early games are nearly always problematic. They were not like blockbuster movies that have a stark "release date" when suddenly you could find them everywhere. If you look at the way I dated the anniversary of D&D, it is all based on things like when the first ads appeared, when "coming soon" notices appeared, and from that really the best I could do was just to sketch boundaries around a period of time. It's hard to say a game was available if no one knows about it, which is why I like ads, especially for things that were effectively mail-order products. But they can also present a sort of a chicken-and-egg problem: advertisements need to be sent in to periodicals in advance, and given how amateurish the hobby was, it is hard to know when periodicals were actually published (as opposed to the month on the cover), whether people advertised things that were actually done, and thus how well advertisers timed the availability of their games versus their marketing.
My Chainmail date is really no better than any of my other dates for these things. I know I spilled quite a bit of ink in PatW on the date for Blackmoor's inception, and I could have done the same for Chainmail. A March date was already around in earlier looks at the history of the game, and what I saw was consistent with that. My date was, following Zenopus's lead above, based in no small part on the earliest advertisements for Guidon Games, which appeared in the April International Wargamer and a few other contemporary places. But that has to be understood in terms of how the IW production schedule operated at the time, and who got which issues when. The short story is that I concluded that the March and April IWs were produced and shipped simultaneously - so effectively, there was no issue shipped in March - and that IW production had a long lead-time, maybe up to six weeks between layout and issues being in people's hands. There are good data points to suggest that the March and April IWs were jointly in subscribers' hand by the third or so week of April. Note that the April IW ad lists Chainmail as available, but suggests that Alex and Dunkirk were scheduled for an April 30 release - something you would not bother to mention if you expected your mail-order ad to be seen like April 18th. But these are ultimately indirect data points, and to be absolutely clear, they don't rule out an April "release" date for Chainmail - if you're counting from when just anyone could have ordered it, it wouldn't be until after they saw an ad.
That was my reasoning ten years ago when I was writing that part of PatW, anyway. I have seen more data points since, but in order to avoid the drama mentioned above, I'll only remark that Dave Arneson was not "just anyone", and that he was surely aware of Chainmail before April. That much said, let me reiterate - dating for these things is really problematic, and arguing for an April "release" is not inherently an untenable position. The month of May, well, that would seem pretty unlikely.
Most else of what I'd say here has already been said.