Answer: Plant material (probable derived from bananas)
Congratulations to everyone who wrote in - you all got this one right! Alasdair rightly said "Is that not just plant material? The beginnings of parasitosis of the delusional variety if it is. Advise the patient not to worry."
While these structures are commonly referred to as banana 'seeds', the Cavendish bananas that are most often sold in grocery stores do not actually develop seeds. They have been bred to be sterile. However, each aborted ovum has a vascular network consisting of xylem strands and associated cells containing astringent tannins. Upon ripening, the tannins polymerize into a semi-solid mass called 'tannin bodies' which fill the cells. The tannin bodies sometimes incorporate red-brown pigments from polyphenol oxidase activity (like the browning reaction in cut apples) as the cells age, and can therefore be seen as the red-brown bodies in this case. They are associated with the xylem strand which give them a chain-like appearance.
Anonymous Anonymous also commented "They resemble arthroconidia still stuck together. Is there a reference book for such things?"
There are a few references out there you might find helpful.
In my opinion, the best reference is the "Atlas of Human Parasitology" by Ash and Orihel which has a nice section on parasitology mimics and artifacts (although it incorrectly calls the structures in the case banana 'seeds'). These authors also have another excellent atlas called "Parasites in Human Tissues" which has a section on parasite mimics. These 2 atlases are a MUST-have for those interested in parasitology.
Another book that has some nice images is "Atlas of Microscopic Artifacts and Foreign Materials" by I-Tien Yeh.
Finally, here is a link to a short paper I wrote a while back that shows the histologic appearance of a peanut, blueberry, lentil, and hotdog: Pritt et al.