We use QCD sum rules to study the recently observed resonance-like structures in the π + χ c 1 mass distribution, Z 1 + ( 4050 ) and Z 2 + ( 4250 ) , considered as D ∗ + D ¯ ∗ 0 and D 1 + D ¯ 0 + D + D ¯ 1 0 molecules with the quantum number J P = 0 + and J P = 1 − , respectively. We consider the contributions of condensates up to dimension eight and work at leading order in α s . We obtain m D ∗ D ∗ = ( 4.15 ± 0.12 ) GeV , around 100 MeV above the D ∗ D ∗ threshold, and m D 1 D = ( 4.19 ± 0.22 ) GeV , around 100 MeV below the D 1 D threshold. We conclude that the D ∗ + D ¯ ∗ 0 state is probably a virtual state that is not related with the Z 1 + ( 4050 ) resonance-like structure. In the case of the D 1 D molecular state, considering the errors, its mass is consistent with both Z 1 + ( 4050 ) and Z 2 + ( 4250 ) resonance-like structures. Therefore, we conclude that no definite conclusion can be drawn for this state from the present analysis.