I assure you that there are not only obligate chemoautotrophs, but that they are quite common. Probably 80% of the microbes I grow in the laboratory are chemoautotrophs.
Life requires, at a minimum:
1. an oxidant - for aerobes that's oxygen, but under anaerobic conditions assorted things can also be used, such as sulfate, elemental sulfur, nitrate, nitrite, carbon dioxide - ALL inorganic.
2. a reductant - for heterotrophs like us - sushi. For autotrophs, hydrogen gas, hydrogen sulfide, nitrite, ammonia, other reduced metals - ALL inorganic.
3. source of carbon. For heterotrophs like you - sushi. For autotrophs, carbon dioxide, sometimes carbon monoxide. You can quibble about CO, but carbon dioxide IS inorganic.
Classes:
Photoautotrophs. Plants, Cyanobacteria and assorted anaerobic sulfur bacteria. Light is the source of energy, oxygen is evolved and carbon dioxide is fixed to organic carbon.
Chemoautotrophs. Assorted bacteria - some aerobic and some anaerobic. Nitrifying bacteria, assorted sulfur bacteria, iron oxidizing bacteria, methanogens, etc.
All of these can be grown quite well in media containing NO organic carbon.
Get an Introductory Microbiology book and read the sections on autotrophs (I suggest The Biology of the Prokaryotes). I hope this will help to educate you concerning autotrophy.
This medium will successfully grow Nitrosomonassp.
Ammonium sulfate 2 g/l
Magnesium sulfate 0.5 g/l
Ferrous sulfate .03 g/l
NaCl .3 g/l
Magnesium carbonate 10 g/l
dipatassium phosphate 1 g/l
water 1 liter
adjust pH to 7.3
There are NO organic ingredients for this culture medium. In addition, and especially for Nitrosomonas, organic chemicals are often inhibitory for autotrophic growth.
In addition, I think you should check out lichens. They are a symbiotic relationship consisting of a fungus and an alga. The fungus makes up most of the thallus but relies on the autotrophic activity of the alga for nutrients. And, BTW, there are many places where lichens grow, where there are no pine trees, i.e. tundra.
Leave me out of it.