Chaotic responses induced by an applied rf signal on the long Josephson junction influenced by a constant dc-driven field are investigated by means of a model based on the sine-Gordon equation. We assume that the localized nonlinear excitations present in the system as initial data are the breatherlike mode. Thus, in order to analyze in detail the onset of the complicated irregular behavior (chaos), we employ collective coordinate theory to derive the total Hamiltonian and the dissipative function in terms of the breather width. The appearance of chaos in this system is predicted by the Melnikov theory and a few numerical treatments. A threshold for chaos as a function of the physical parameters of the system is found. Finally, the Poincaré sections, which allow us to see clearly the phenomenon in the nondissipative case, is compared to the analytical prediction and good agreement is obtained.