In this work we study the possible QCD exotic states in the doubly charmed baryon sector. Within chiral effective theory, it is predicted that several excited baryons result from the S-wave scattering of ground-state doubly charmed baryons (Ξcc++,Ξcc+,Ωcc+) and light pseudoscalar mesons (π, K, η). The excited doubly charmed baryons can be classified by the strangeness (S) and isospin (I) quantum numbers. Two of the excited states are clearly exotic, in the sense that they cannot be explained by the conventional baryons with three quarks, since their quantum numbers are (S,I)=(1,0) and (−1,1). Similar to the charmed scalar meson Ds0*(2317) in DK scattering and the hyperon Λ(1405) in K¯N scattering, one bound state below the ΞccK¯ threshold is predicted in the (S,I)=(−1,0) channel. In addition, two resonant structures are found in the Ξccπ,Ξccη, and ΩccK coupled-channel scattering with (S,I)=(0,1/2). The corresponding pole positions and coupling strengths of the excited doubly charmed baryons are given. The scattering lengths of the ground-state doubly charmed baryons and light pseudoscalar mesons are also predicted. The current study may provide useful guides for future experimental measurements and lattice simulations.