What process does deep sea organisms depend on?

A lot of organisms that thrive in the deepest parts of the ocean rely heavily on chemosynthesis.

Chemosynthesis is most commonly seen near thermal vents and involves the biological conversion of 1+ carbon molecules (methane/CO2) and nutrients into organic matter. This is made possible through the oxidation of inorganic molecules such as H2 or Hydrogen Sulfide; these are used as a source of energy, rather than radiation from the sun.