Final answer:
The sympathetic preganglionic neuron that goes directly to an organ without synapsing in the chain ganglia is a branch of the greater splanchnic nerve, which projects onto the celiac ganglion.
Step-by-step explanation:
The only sympathetic preganglionic neuron to go directly to an organ is one branch of the greater splanchnic nerve. Unlike most other preganglionic fibers, which synapse at the level of the sympathetic chain ganglia, this nerve contains fibers that bypass the chain ganglia and directly project onto a collateral ganglion, specifically the celiac ganglion. This pathway is essential for regulating the physiological functions of the digestive organs, as these nerves carry signals that result in changes appropriate for sympathetic activation, such as decreasing digestive activity during stress.