I will discuss polynomials PN of degree N that satisfy non-Hermitian orthogonality conditions with respect to the weight (z+1)N(z+a)Nz2N on a contour in the complex plane going around 0. These polynomials reduce to Jacobi polynomials in case a = 1 and then their zeros cluster along an open arc on the unit circle as the degree tends to infinity. For general a, the polynomials are analyzed by a Riemann-Hilbert problem. It follows that the zeros exhibit an interesting transition for the value of a = 1/9, when the open arc closes to form a closed curve with a density that vanishes quadratically. The transition is described by a Painlevé II transcendent. The polynomials arise in a lozenge tiling problem of a hexagon with a periodic weighting. The transition in the behavior of zeros corresponds to a tacnode in the tiling problem. This is joint work in progress with Christophe Charlier, Maurice Duits and Jonatan Lenells and we use ideas that were developed in [2] for matrix valued orthogonal polynomials in connection with a domino tiling problem for the Aztec diamond.