The chemical reaction between HCl and methyl orange can be represented as follows:
$$HCl + H_2O \rightarrow H_3O^+ + Cl^-$$
$$H_3O^+ + Methyl\ orange \rightarrow H_2O + Methyl\ orange^+$$
In this reaction, the H3O+ ions from the HCl react with the methyl orange molecules to form water and methyl orange+ ions. The methyl orange+ ions are yellow, which is why the solution turns yellow when HCl is added.