  The study of {\em balls-into-bins processes} or {\em occupancy problems} has
a long history. These processes can be used to translate realistic problems
into mathematical ones in a natural way. In general, the goal of a
balls-into-bins process is to allocate a set of independent objects (tasks,
jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to
minimize the maximum load. In this paper, we analyze the maximum load for the
{\em chains-into-bins} problem, which is defined as follows. There are $n$
bins, and $m$ objects to be allocated. Each object consists of balls connected
into a chain of length $\ell$, so that there are $m \ell$ balls in total. We
assume the chains cannot be broken, and that the balls in one chain have to be
allocated to $\ell$ consecutive bins. We allow each chain $d$ independent and
uniformly random bin choices for its starting position. The chain is allocated
using the rule that the maximum load of any bin receiving a ball of that chain
is minimized. We show that, for $d \ge 2$ and $m\cdot\ell=O(n)$, the maximum
load is $((\ln \ln m)/\ln d) +O(1)$ with probability $1-\tilde O(1/m^{d-1})$.
