It has been widely suggested that life based around carbon, hydrogen, oxygen, and nitrogen is the only plausible biochemistry, and specifically that terrestrial biochemistry of nucleic acids, proteins, and sugars is likely to be "universal." This is not an inevitable conclusion from our knowledge of chemistry. I argue that it is the nature of the liquid in which life evolves that defines the most appropriate chemistry. Fluids other than water could be abundant on a cosmic scale and could therefore be an environment in which non-terrestrial biochemistry could evolve. The chemical nature of these liquids could lead to quite different biochemistries, a hypothesis discussed in the context of the proposed "ammonochemistry" of the internal oceans of the Galilean satellites and a more speculative "silicon biochemistry" in liquid nitrogen. These different chemistries satisfy the thermodynamic drive for life through different mechanisms, and so will have different chemical signatures than terrestrial biochemistry.