We use two nonlinear recurrence relations to define the same sequence of polynomials, a sequence resembling the Chebyshev polynomials of the first kind. Among other properties, we obtain results on their irreducibility and zero distribution. We then study the 2×2\documentclass[12pt]{minimal}
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\begin{document}$$2\times 2$$\end{document} Hankel determinants of these polynomials, which have interesting zero distributions. Furthermore, if these polynomials are split into two halves, then the zeros of one half lie in the interval (-1,1)\documentclass[12pt]{minimal}
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\begin{document}$$(-1,1)$$\end{document}, while those of the other half lie on the unit circle. Some further extensions and generalizations of these results are indicated.
