  We construct a simple closed-form representation of degree-ordered system of
bivariate Chebyshev-I orthogonal polynomials $\mathscr{T}_{n,r}(u,v,w)$ on
simplicial domains. We show that these polynomials $\mathscr{T}_{n,r}(u,v,w),$
$r=0,1,\dots,n;$ $n\geq 0$ form an orthogonal system with respect to the
Chebyshev-I weight function.
