Yes. A molecule does exist that is composed of two oxygen atoms and one hydrogen atom bonded together. The substance is called hydroperoxyl radical and can be represented as HO2. Covalent bonds hold the two oxygen atoms and one hydrogen atom together. The substance is the "protonated form of superoxide". It may also be formed by removing a hydrogen atom from hydrogen peroxide.
Hydroperoxyl is quite reactive. Thus, it is involved in chain reactions within the atmosphere. For example, in the stratosphere, HO2 is involved in ozone-destroying chain reactions. In the troposphere, the substance is formed as an intermediate molecule within the chain reaction that occurs when hydrocarbons are oxidized. Hydroperoxyl is also involved in the metabolic oxidative damage that occurs to phospholipid fatty acid chains that make up phospholipid bilayers of cell membranes.