What attractive force holds two hydrogen atoms and one oxygen atom together to make the substance water?

Answer: covalent chemical bonds.

Justification:

1) The attraction between atoms is a chemical bond. That is how chemical compounds are formed.

2) The chemical bond may be ionic (between ions), covalent (sharing electrons), or metallic (only between metal elements).

3) Hydrogen and oxygen being both non-metals, do not have the ability to remove completely electrons from each other, so they do not form ionic bonds. Instead, they form covalent bonds by sharing electrons to both of them fill their valence electron shell (octet rule).

In particular, since the electronegativities of hydrogen and oxygen are relatively high (but not as high as to form ions), the electrons are not evenly shared. The electrons are pulled with more force by oxygen (more electronegatiive than hydrogen) and so hydrogen and oxygen form polar covalent bonds.

Chemical bonding is the answer