Manny from Petach Tikva asks:

May I use sh’mittah
olive oil for lighting the Chanukah menorah?

Sh’mittah oil may be used for lighting (see Chapter 8,
Mishna 2 of Tractate Shvi’is). One is deriving a commonly enjoyed
benefit from the oil while it is being consumed (hano’oso ubiuro shoveh).
One may therefore use sh’mittah olive oil for Shabbos and Yom
Tov
lights. Thus it follows that when lighting lights from which no benefit
is or may be derived, sh’mittah oil may not be used. For this reason, one
may not use sh’mittah oil for the Chanukah lights, since it is forbidden
to derive benefit from them. By the same token, it is forbidden to use this oil
for a yahrzeit (memorial) light. The custom is to allow this light to
burn during the day, when light is not needed for illumination. It would also be
forbidden to use sh’mittah oil for the Ner Tomid (a light which is
constantly burning in the synagogue). This light is also not intended for
illumination but rather for the honour of the holy place. However, Rav Shlomo
Zalman Auerbach, o.b.m., does permit using sh’mittah olive oil for
Chanukah and for the Ner Tomid – see Minchas Shlomo 1:42.