The Collaborative International Dictionary of English v.0.48:

Thallus \Thal"lus\, n.; pl. Thalli. [NL., fr. Gr. ? young
   shoot or branch, frond.] (Bot.)
   A solid mass of cellular tissue, consisting of one or more
   layers, usually in the form of a flat stratum or expansion,
   but sometimes erect or pendulous, and elongated and
   branching, and forming the substance of the thallogens.
   [1913 Webster]