Thanks, all, for the responses. I just assumed that the requirement
was a safety feature in the more traditional (circuit overload)
sense. I'm going to be using this freezer for my beer kegs, so a
normal freezer alarm won't work (they trigger when the temp rises
above, say, 15 degrees. This will typically be around 40). I'll
probably just cobble together a simple 'lost power' alarm.

Curiously, my upright freezer has a built in temperature alarm.
Unfortunately, it's AC powered, so it would be useless in the
described scenarios.

In article om,
says...

FREEZER ALARMS?
1) http://www.shiptheweb.com/Gifts/Prod...FQufbgodFBmdyw
2) http://www.cabelas.com/prod-1/0017651515725a.shtml (Appears similar
to item 1) and has on/off switch.
3) Also models (google search) that will dial up to four telephone
numbers if freezer temp outside limits.
Prices for 1 and appear to be $10 to $20 plus shipping.
One of theses might be an alternative if it is just not possible to
install a separate circuit?
Chest type freezers in particular are often poked away out of regular
sight in garage or basement storage area; by the time one finds
freezer not working there may be a soggy mess of unusable/unsafe food?