His students include David Gross, one of the winners of the 2004 Nobel Prize in Physics, and John H. Schwarz, one of the pioneers of string theory.

Chew's central contribution to the program came in 1961:[5] along with collaborator Steven Frautschi, they noted that the mesons fall into families (straight-line Regge trajectories) where the square of the mass of a meson is linearly proportional to the spin (in their scheme, spin is plotted against mass squared on a so-called Chew–Frautschi plot), with the same constant of proportionality for each of the families.

Since bound states in quantum mechanics naturally fall into families of this sort, their conclusion, quickly accepted, was that none of the strongly interacting particles were elementary.

The conservative point of view was that the bound states were made up of elementary particles, but Chew's more far-reaching vision was that there would be a new type of theory which describes the interactions of bound-states which have no point-like constituents at all.

He stated that an "appeal to God may be needed to answer the 'origin' question, 'Why should a quantum universe evolving toward a semiclassical limit be consistent?'"