What's a good, low-maintenance option for a small herb garden/grow box?

[Retrograde]

10. Basil is an annual

but basil plants are easy to find in nurseries, and they grow well in pots. I've kept one plant going until November by moving it around, but I don't expect to keep them over winter - even in California.

I use plastic pots that nurseries use - they can be cleaned and reused. And if you know someone who gardens, they probably have some they want to get rid of.

Parsley tends to have large taproots, but with a deep enough pot it might be possible - I've always done it in the ground. Chives seem to do well (unless the cat decides to eat them), but my pot-grown ones never seem to get very thick. They do blossom occasionally, and steeping the blossoms in vinegar will give you something of the taste of chives.

Have you considered vegetables as well? Plant growers have developed hybrid tomatoes that do well in pots (and, in their native lands tomatoes are perennials, so it should be possible to keep them inside in the winter. They do need sun to set and ripen fruit though) as well as peppers. I'm doing a lot more container gardening, since my soil is what's called adobe, and I've gotten respectable crops of peppers, tomatoes, and eggplants.