General SQL (SQLite): Sum/Count based on values in the dataset

I have a database in SQLite (which supports subqueries and standard aggregate functions).

One table describes the structure (chapters), one stores answers to questions, related to each chapter, and one table stores answer types. I want to get out data on each chapter, with a count on each of the values in the answer type table.

The data model is (simplified) like this:

Table Structure
+-------------+------------+
| Field       |  Type      |
+-------------+------------+
| Chapter     | int        |
| Description | varchar    |
+-------------+------------+
 
Table Answer
+-----------+----------+
| Field     |  Type    |
+-----------+----------+
| Answer    | int      |
| Chapter   | int      |
+-----------+----------+
 
Table AnswerOption
+-------------+------------+
| Field       |  Type      |
+-------------+------------+
| AnswerOptId | int        | (relates to Answer.Answer)
| Description | varchar    |
+-------------+------------+


I would really like one(!) query that gives a result like this:
+---------+---------+---------+---------+---------+
| Chapter | Value 1 | Value 2 | Value 3 | Value 4 |
+---------+---------+---------+---------+---------+
|       1 |       3 |       2 |      15 |       6 |
|       2 |      11 |       0 |       7 |      16 |
|       3 |       6 |       1 |      12 |       1 |
+---------+---------+---------+---------+---------+
Where Value N corresponds to each row in the AnswerOption table.

Please let me know if you need more information - the question is complicated to explain, but might be even harder to crack :)

Br,
Henrik