We study the relationship between the D∗s0(2317)+ resonance and the decay of the Bc meson into J/ψDK. In this process, the Bc meson decays first into J/ψ and the quark pair cs¯, and then the quark pair hadronizes into DK or D_sη components, which undergo final state interaction. This final state interaction, generating the D∗s0(2317)+ resonance, is described by the chiral unitary approach. With the parameters which allow us to match the pole position of the D∗s0(2317)+, we obtain the DK invariant mass distribution of the decay Bc→J/ψDK, and also the rate for Bc→J/ψD∗s0(2317). The ratio of these two magnitude is then predicted.