  The Sachdev-Ye-Kitaev (SYK) model provides an uncommon example of a chaotic
theory that can be analysed analytically. In the deep infrared limit, the
original model has an emergent conformal (reparametrisation) symmetry that is
broken both spontaneously and explicitly. The explicit breaking of this
symmetry comes about due to pseudo-Nambu-Goldstone modes that are not exact
zero-modes of the model. In this paper, we study a version of the model which
preserves the reparametrisation symmetry at all length scales. We study the
heavy-light correlation functions of the operators in the conformal spectrum of
the theory. The three point functions of such operators allow us to demonstrate
that matrix elements of primaries ${\cal O}_n$ of the CFT$_1$ take the form
postulated by the Eigenstate Thermalisation Hypothesis. We also discuss the
implications of these results for the states in AdS$_2$ gravity dual.
