We study the influence of the D-s0*(2317)(+) resonance in the decay B-c -> J/psi DK. In this process, we consider that the B-c meson decays first into J/psi and the quark pair c (s) over bars, and then the quark pair hadronizes into DK or D-s eta components. The final state interaction, generating the D-s0*(2317)(+) resonance, is described by the chiral heavy meson unitary approach. With the parameters chosen in order to match the pole position of the D-s0*(2317)(+), we obtain the DK invariant mass distribution of the decay B-c -> J/psi DK, and also the rate for B-c -> J/psi D-s0*(2317). We predict the ratio of these two magnitudes. This decay mechanism has not been measured yet, and it would provide insight about the nature of this resonance.