Chem equation

There will be a white precipitate of silver chloride, with chemical formula AgCl.

When the three compounds dissolve in water, there are NH4+, Cl-, H+, NO3- and Ag+ ions in the solution. When Ag+ and Cl- ions combine together, the AgCl formed is insoluble in water and thus a white precipitate is formed.
Ag+(aq) + Cl-(aq) → AgCl(s)

Other combinations of cation and anion give soluble substances (i.e. NH4Cl, NH4NO3, HCl, HNO3 and AgNO3), and they will dissociate again to give back the cations and anions.