One point worth considering from the post you reply to refers to "the grid" rather than minis in particular - which I don't think Chainmail or OD&D reference at all.
Chainmail was being played as a traditional wargame with miniatures - so measuring tape and rulers, but not a grid.
If anyone can find me references in an official rulebook to using a grid for combat before the 1995 Combat & Tactics book, I'd appreciate it. I'm sure people did do it, as play was so varied,
It's in the 1981 Moldvay Basic rules. It doesn't go into much detail on the
use of a grid, but on B61 on the second page of the Dungeon Mastering as a Fine Art appendix of suggestions and advice, under PLAYING SURFACE, we find the first recommendation of using large sheets of graph paper with a 1" = 5' scale, for combat specifically. This is an optional suggestion, though, not an official "this is how to play" rule. This combined with the combat and movement rules (particularly Encounter Movement and Defensive Movement on B24-25) is enough to run combat movement on a grid, although there is no discussion of distances on the diagonal like there was in 3rd ed. Interestingly, The Haunted Keep, the sample mini-adventure in that book, also uses a 1" = 5' grid scale, unlike most other TSR publications.
I'd also be interested when rules were first published assuming gridded battlemaps. I think that using grids (e.g. Chessex battle maps, reverse sides of wrapping paper, etc.) probably started to become popular when modules publishing gridded maps (was Keep on the Borderlands the first instance of this?). I think it is natural to want to represent what one saw in the module on a larger scale with minis.
Gridded
maps date back to the very first published adventures. Dave Arneson's Temple of the Frog from
Supplement II: Blackmoor (1975), Jennell Jaquays'
F'Chelrak's Tomb, and Wee Warriors'
Palace of the Vampire Queen (both June 1976, the first third party published adventures), as the earliest examples.
Whether these constitute the "battlemaps" you're thinking of I'm less clear on. The maps for Temple of the Frog are rough, don't have a grid scale printed on them, and clearly squeezed from letter size sheets to fit into the digest-sized booklet. The first (large area exterior) map seems to be at some larger scale- quite possibly 15' squares. the interior ones look to be
roughly 10' squares, but the map is imprecise and doesn't conform exactly to the grid.
The published scale for stuff going back to the 70s was mostly 10' per square on graph grids with a 1/4" square print. IIRC
F'Chelrak's Tomb is an unusual exception, and is actually printed with a 5' grid scale, so Jaquays may once again have been ahead of the curve. I know she was into painting and playing with miniatures, but I don't know if that was true all the way back in '76.