Unmodifiable meaning that any ingame actions have no result on the terrain.
Like in Source games.
Question: Should I export one large model of the map, or should I split it into smaller chunks? If so, how?
Given that you have tagged the question as "rendering", I will say it depends on the poly count of the terrain.
If rendering the entire terrain causes problems due to high poly count, then chunk it, and perform visibility checks on each chunk. This may, in turn, allow you to increase the poly count of each chunk, thereby improving how it looks.
However, given that you have also tagged the question as "physics" engine, you may want to keep the poly count of each chunk down, in order to make collision detection cheaper.
Coincidentally, chunking is how open world, voxel based games (like Minecraft) work.