Weird Line Between Meshes

Hi everyone! Sorry if this is a noob-ish question, but I don't even know how to go about searching for this problem.

I'm making a runner for mobile, where the player is traveling down a river. To have the river itself looping, I have several chunks of ground-river-ground that get placed next to each other and looped around. For gameplay reasons, the chunks need to be relatively small (I have 12 of them that cover the length of the screen). I'm noticing something strange between the ground pieces, however. No matter where I place the chunks in relation to each other, there are occasional lines between them that appear to be the texture on the side of the ground peeking through.

These are close-up screens of two of my meshes lined up with each other. The screen on the left shows them disconnected, so you can see what the model looks like on the side. The middle screen shows the models when they're right next to each other. I zoomed in as much as I could and have the coordinates as close as Unity allows me to. However, that green line still shows up in the middle (which I believe to be the side of the model peeking through). One might assume that they're simply not lined up correctly, which is why I've included the third screen - that screen shows the two models overlapping significantly (as you can see by the blue line of the mesh on the right) - and the green line is still there.

The line isn't constant - it's not always visible, only at certain camera angles/positions - but on mobile I see the lines quite consistently as the game moves forward. The model is a very simple rectangular box - 24 verts, 12 tris. I've tried several different shaders, different texture compression settings, etc. and I can't think of any reason why this might be happening. Would something like this be the result of weirdness with the model, or maybe with the texture? Or is there some setting I need to check in Unity?

Thanks in advance for any assistance :)