  We study the spread of R\'enyi entropy between two halves of a
Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield
double (TFD) state. The SYK chain model is a model of chaotic many-body
systems, which describes a one-dimensional lattice of Majorana fermions, with
spatially local random quartic interaction. We find that for integer R\'enyi
index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically
smaller value than expected. This implies that the TFD state of the SYK chain
does not rapidly thermalize, despite being maximally chaotic: instead, it
rapidly approaches a prethermal state. We compare our results to the signatures
of thermalization observed in other quenches in the SYK model, and to intuition
from nearly-$\mathrm{AdS}_2$ gravity.
