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The primary motivation of the paper is to define a new class Chδα,β,γ which consists of univalent functions associated with Chebyshev polynomials. For this class, we determine the coefficient bound and convolution preserving property. Furthermore, by using subordination structure, two new subclasses of Chδα,β,γ are introduced and denoted by Mλ1,λ2,s and Nλ1,λ2,s, respectively. For these subclasses, we obtain coefficient estimate, extreme points, integral representation, convexity, geometric interpretation, and inclusion results. Moreover, we prove that, under some restrictions on parameters, Chδα,β,γ=Nλ1,λ2,s.