presence of positive topological entropy implies chaos in the sense of Li-Yorke. Moreover, Li-Yorke chaos on several spaces in connection with the cardinality of its scrambled sets was studied within the scope of the paper [24]. Besides, Li-Yorke sensitivity, which links the Li-Yorke chaos with the notion of sensitivity, was studied in the paper [11]. The studies [3, 4, 5, 7, 8, 9, 10] were concerned with the extension of chaos in continuous-time systems that possess asymptotically stable and hyperbolic equilibria as well as orbitally stable limit cycles. It was found in these papers that the solutions admit the same type of chaos as the perturbations. The paper [5] deals with the general technique of dynamical synthesis, which was developed in [17]–[20]. In the present study, we develop the concept of Li-Yorke chaos for DETS and prove its existence rigorously. Our results are appropriate to obtain chaotic DETS with arbitrary high dimensions. Throughout the paper, we will denote by R , Z and N the sets of real numbers, integers and natural numbers, respectively. In this study, we consider the following equation, where A is a constant n × n real valued matrix, the function f : T 0 × R n → R n is rd-continuous and the function g ( t, ζ ) is defined through the equation g ( t, ζ ) = ζ$_{k}$ for t ∈ [ $^{θ$_{2}$$_{k}$}$− $_{1}$, θ$_{2}$$_{k}$ ] , k ∈ Z , such that ζ = { ζ$_{k}$ } is a sequence generated by the map where ζ$_{0}$ ∈ Λ , F : Λ → Λ is a continuous function and Λ is a compact subset of R $^{n}$. In equation (1.1) the time scale T 0 is defined as T 0 = ⋃ ∞ k $^{=}$−∞ [ $^{θ$_{2}$$_{k}$}$− $_{1}$, θ$_{2}$$_{k}$ ] in which { θ$_{k}$ } is a strictly increasing sequence of real numbers such that | θ$_{k}$ | → ∞ as | k | → ∞ and ∑ −∞ ( θ$_{2}$$_{k}$ − $^{θ$_{2}$$_{k}$}$− $_{1}$) = ∞ , ∑ ∞$_{(}$$_{θ}$$_{2}$$_{k}$ − $^{θ$_{2}$$_{k}$}$− $_{1}$) = ∞ . In the present paper, we investigate the existence of chaos in the dynamics of equation (1.1). The system under discussion is a hybrid one, since it combines the continuous dynamics on the time scale with the discrete equation used in the right hand side of the system. We theoretically prove that chaos exists in (1.1) provided that the map (1.2) is chaotic. For that purpose, we make use of the reduction technique to impulsive differential equations, which was presented by Akhmet and Turan [1]. As far as we know, there is no paper on chaos in dynamics on time scales. The reason is that the dynamics is essentially non-autonomous and it is difficult to verify the ingredients of chaos for unspecified time scales. That is why we utilize the time scale introduced in the papers [1, 2] and the method of reduction of the dynamics to impulsive differential equations [1]. The rest of the paper is organized as follows. In Section 2, some preliminary results as well as basic concepts about DETS are mentioned. Section 3 is devoted to the bounded solutions of (1.1). In Section 4, we give the description of the chaos of equation (1.1) and prove its presence rigorously. An example y $^{Δ}$( t ) = Ay ( t ) + f ( t, y ( t )) + g ( t, ζ ) , t ∈ T $_{0}$, (1.1) ζ$_{k}$$_{+1}$ = F ( ζ$_{k}$ ) , (1.2) 2