A new non-local integrable chain with continuous time and discrete space variable is considered. In contrast to the case of Toda and Volterra chains, the general solution can be presented in explicit form in terms of two arbitrary sequences. It is shown that this solution is connected with the so-called Uvarov-Chihara problem (inserting a discrete mass at the centre of the spectral interval of symmetric orthogonal polynomials). The asymptotic behaviour of the recurrence coefficients of such polynomials is considered.