'oirQuoting FDR:
A few of my tomato plants have developed brown spots and yellowing, which
according to a book on tomato problems I have, appears to be Gray Leaf Spot
or Early Blight. It seems more like the former.

I would suggest that you take a look at the below website, if you're
not already familiar with it:

http://aggie-horticulture.tamu.edu/tomatoproblemsolver/

Anyway, they say to plant resistant varieties or rotate crops, but list
either as a disease to be treated with fungicide. What fungicide do you use
to treat this? Would it be chemical or natural?

I use Daconil (aka Ortho Garden Disease Control). Once a week spray
as a preventative. Must be applied so as to coat all plant surfaces
(it is not systemic) it 'seals' the plant.

It is not 'organic', but as far as toxicity goes, I am comfortable
with using it -- more comfortable than say rotenone, or pyrethrins
(organic) for example.

It also helps to only water the plants in the early part of the day so
that the foliage can quickly dry. Mulching is also helpful as it
limits splash back of fungal spores from soil.