SELECT syntax question - combining COUNT and DISTINCT

I'm having some trouble working with aggregates. I think I'm missing
the concept of how aggregates are treated. Is there a tutorial page?

Here's my problem, no doubt very simple. It's one table only, nice and
easy...
SELECT DISTINCT pdb_id FROM chain WHERE chain_id = 'A';

But now I want to count how many records are returned and I can't work
it out. I'm sure I'm missing something obvious.
For instance "SELECT COUNT(pdb_id) FROM chain WHERE chain_id = 'A';"
works fine but of course is no longer distinct.

A secondary question (relating to my quality control problem but not
the subject heading) is why I can't do this:
"SELECT DISTINCT chain_id FROM chain WHERE pdb_id IN (SELECT pdb_code
FROM pdb_entry WHERE chain_count=1);"
This looks OK but takes apparently forever (or until I lose patience)
on my Mac G4. There are about 10,000 values in that subquery, so I
didn't expect it to be lightning fast, but it seems ridiculous.

Relevant snippets of table:
pdb_entry - 19,587 entries
---------
pdb_code is KEY, CHAR(4), unique, indexed
chain_count is INTEGER

chain - 40,844 entries
-----
pdb_id is CHAR(4) Foreign key, indexed
chain_id is CHAR(1)

Cath Lawrence, Cath(dot)Lawrence(at)anu(dot)edu(dot)au
Senior Scientific Programmer, Centre for Bioinformation Science,
John Curtin School of Medical Research (room 4088)
Australian National University, Canberra ACT 0200
ph: (02) 61257959 mobile: 0421-902694 fax: (02) 61252595