Shemitta Oil For Lighting Chanukah Candles
The mishna in the beginning of the eighth perek of Shvi'it lists the permissible uses for shemitta produce: eating, drinking, smearing lotions, lighting candles for light, and dyeing. Though the Torah only delineates eating (and drinking and smearing are implied, as they are comparable to eating), by adding the term 'lakhem' ('lakhem le-akhla') the Torah broadens the category to include additional varieties of benefit. The gemara in Sukka (40), however, imposes one requirement: the benefit must be drawn in a manner which allows simultaneous benefit and consumption (hana'atan u-biuran shaveh). This type of benefit closely resembles eating and is therefore allowed. Non-simultaneous benefit and consumption (such as using shemitta as firewood for fuel) deviates too sharply from the paradigm of eating to be allowable.
Presumably, based upon these criteria, shemitta oil may not be used for hadlakat neirot on Chanukah. The gemara in Shabbat (21a) specifically prohibits direct benefit from neirot Chanukah. Hence, utilizing shemitta oil is an act of destruction and violates the principle of le-akhla ve-lo le-hefsed. Indeed, this is the basic ruling stated by the Pe'at Ha-shulchan (siman 5 se'if 9) and echoed by many later poskim.
In his sefer, Minchat Shlomo, Rav Shlomo Zalman Auerbach zt"l cites a possible proof to this concept from a Yerushalmi in the beginning of Arla which questions whether an olive tree planted for Chanukah oil is forbidden under the category of Arla. Presumably, as Arla applies only to trees planted for human use and Chanukah oil is forbidden to use, these trees might be exempt from the prohibition. Likewise, as Chanukah oil may not provide human benefit, it does not constitute productive benefit to allow employment of shemitta produce.
There are, however, two possible ways of disputing this position and allowing shemitta oil for hadlakat ner Chanukah. One strategy is to question the scope of the prohibition of benefiting from ner Chanukah. The gemara prohibits counting money by the light of the Chanukah candles. Would this prohibition extend to other forms of use, as well? The Ba'al Hama'or allows using Chanukah candles for tashmishei mitzvah (for the performance of a mitzvah). Other Rishonim disagree with this extreme leniency but do allow certain limited forms of benefit. Would these uses be sufficient to permit the use of shemitta oil?
Beyond the basic halakha allowing certain limited uses, the minhag of shamash may also affect our situation. The Shulchan Arukh (673:1) instructs that a shamash be lit so that if any benefit is received from the light of the menorah, it will be drawn from the shamash and not from the Chanukah candles. The Taz questions this halakha, arguing that undoubtedly the light from the Chanukah candles is stronger than the light from the lone shamash (certainly on the concluding days of Chanukah). Hence, the shamash hasn't solved the problem of benefiting from Chanukah candles, as inevitably 'most' of the benefit still stems from the Chanukah lights themselves. The Taz explains that the prohibition against deriving benefit from the Chanukah candles is not essential in nature, but rather based on peripheral reasons: 1) deriving benefit will demean the mitzvah of hadlaka (bizuy mitzva), or 2) a bystander will witness this benefit and assume that the candles were lit for personal use (thereby undermining the pirsumei nisa component of the mitzva). Hence, by lighting a shamash one does not completely ignore the mitzvah, nor will the average bystander misunderstand the intentions behind his lighting. At this point, then, no prohibition exists against using the Chanukah candles for benefit.
To summarize: although the gemara in Shabbat clearly prohibited benefit from the Chanukah candles, many Rishonim allow certain types of peripheral uses (mitzva uses, benefit at a distance, temporary benefit etc.). Even 'hard-liners' who forbid all use would still allow benefit once the shamash is lit. We might therefore permit utilizing shemitta oil since some degree of benefit is allowable and the oil is not entirely wasted; the condition of le-akhla ve-lo le-hefsed is thus satisfied.
Rav Shlomo Zalman, however, adopts a different strategy to permit shemitta oil, one which accommodates even the most stringent view, which forbids all uses. When the gemara in Sukka allowed uses akin to eating, it did not demand that each and every utility be inspected for its 'benefit quotient.' Instead, certain categories of benefit similar to eating were allowed, and these may be employed even in instances where no actual human benefit exists. Since lighting candles or oil generally serves human benefit, it is permissible even in exceptional cases where no actual human benefit is allowed. He cites the gemara in Bekhorot which forbids the sacrifice of a shvi'it animal (i.e. an animal purchased which shemitta money) since the eimurim (intestines) will be burnt on the mizbeiach and thus yield no human benefit. The act of burning on the mizbeiach typically does not provide human benefit and is therefore forbidden. By contrast, the act of kindling a fire for light generally yields human benefit and is therefore permissible, even in instances in which, for whatever reason, that benefit is denied.