From the ArcaMax Publishing, Gardening Newsletter:
http://www.arcamax.com/news/gardening/s-1901-757559
Question: I live in a third-floor apartment and would like to start an
herb garden. I don't have a balcony, but I do have a window that gets
lots of sunlight. Are there herbs that I can grow year-round indoors?
Answer: Some herbs adapt better than others to growing indoors; basil,
thyme, chives and lemon verbena tend to do well as houseplants. Some
herbs, such as rosemary and sage, will grow fine indoors for a while,
but will tend to get leggy and "tired" after a while. However, you can
root cuttings and start new plants as necessary.