On p. 580 in _The Lord of the Rings: A Reader's
Companion_, Wayne Hammond and Christina Scull writes:
"_athelas_ in the noble tongue [...] In the following
paragraph Aragorn gives the corresponding name of the
plant in Quenya, _asea aranion_ 'leaf of kings'."

The Sindarin name is discussed on p. 183:
"Athelas [...] The first element is problematic;
according to Arden R. Smith, an unpublished etymology
connects it with Quenya _asea_, as in _asea aranion_
'kingsfoil' (but if so, _athelas_ = 'leaf-leaf')."

The translation 'leaf of kings' does not seem to be
attested. The only translation of _asea_ that I know
of is the one quoted by William C. Hicklin on the
art.fan.tolkien newsgroup:
<http://groups.google.com/group/rec.arts.books.tolkien/browse_thread/thread/34fc\
7f494c7ff868/3fad9c3c879f5a2c?lnk=st&q=athelas+hicklin&rnum=1&hl=en#3fad9c3c879f\
5a2c>

"Christopher Tolkien and I have had an ongoing discussion about the origins of
this word. It plainly contains -las 'leaf'. It is possible (but entirely
speculative) that what Tolkien had in mind at that time (1938-39) was the Old
English word aethele 'noble, royal.' This would translate 'kingsfoil,' near
enough. At any rate, a very late note (1970 or later) says that Asea (cf.
Aragorn, 'asea aranion') was the name in Quenya, regularly adapted and
compounded with -las in Sindarin. The plant was known to the medical
loremasters of the Noldor. The root is *ATHAYA, 'helpful, kindly,
beneficial.' "

From this it would seem that _asea_ is in fact an
adjective (perhaps substantivized) meaning *'beneficial'
and that the 'leaf'(or 'foil') part is understood in the
Quenya name:_asea [?lasse] aranion_, 'the beneficial
(leaf) of kings'. But perhaps there are other explanations
as well.

/Fredrik