Grouping, counting and excluding based on column value

Question

Although I've not a complete newbie in SQL or MySQL I notice that there's still quite a bit to learn. I cannot get my head around this one, after much trying, reading and searching. If you can give any pointers, I'd be grateful.

I have simplified the actual data and tables to the following.

Two tables are relevant: Staff, and Work. They contain data on staff in various projects.

Staff:

ID  Name    Unit     

1   Smith   Chicago
2   Clarke  London
3   Hess    Chicago

Work:

StaffID   ProjectID

1          10
2          10
3          10
1          20
2          30
3          40
1          50
3          50

Goal:

To get grouped all those projects where there are staff from Chicago, with the count of all staff in that project.

Expected result:

Project  Staff count

10        3
20        1
40        1
50        2

So the project 30 is not listed because its member(s) are not from Chicago.

My query below is obviously wrong. It counts only those project members who are from Chicago, not the whole project staff.

SELECT 
    work.projectID as Project, COUNT(*) as "Staff count" 
FROM 
    staff 
JOIN
    work ON staff.ID=work.staffID
WHERE
    unit="Chicago"
GROUP BY
    work.projectID;

Answer 1

Finally: the result. Thanks again both @Johan and @a'r for your help, and @Johan for getting me on the right track (in my case).

I changed the sub-select to a derived table, and inner-joined this with the Work table on projectID.

SELECT 
   w.projectID AS project
   ,COUNT(*) AS `staff count`
FROM work w
INNER JOIN 
    (SELECT DISTINCT w2.projectID 
        FROM work w2
        INNER JOIN staff s ON (w2.staffID = s.id AND s.unit = 'Chicago')) c
ON (w.projectID = c.projectID)
GROUP BY w.projectID