Yes, a chemical reaction can happen with only one substance.
A typical example of such reaction is the radioactive decay.
Radioactive decay is the loss of elementary particles from an unstable nucleus, ultimately changing the unstable element into another more stable element. .
When radioactive elements are let alone, they decompose to form stable harmless elements.
An example of radioactive decay is attached in the image below;
A chemical reaction cannot happen with water alone. This is because, a chemical reaction must involve collision of particles from different reactants in order to give a product. No chemical specie can react with itself without some kind of interaction with another chemical specie which may or may not enter into the rate equation for that reaction.
Only nuclear reactions are spontaneous and involve only one reactant for spontaneous radioactive decay.
