An orthogonal Chebyshev kernel function for Support Vector Machine (SVM) is proposed based on extensive research about the properties of kernel functions. Chebyshev polynomials are firstly constructed through Chebyshev formulae. Then based on these polynomials Chebyshev kernels are created satisfying Mercer condition. As Chebyshev polynomial has the best uniform proximity and its orthogonality promises the minimum data redundancy in feature space, it is possible to represent the data with less support vectors. Experimental result shows that compared with other tradition support vector machines, Chebyshev kernel support vector machine performs much better and has less support vectors. Chebyshev kernel also has the ability of generalization. It is proved to be an excellent, widely suited and practical kernel both theoretically and experimentally.