Where did the term cockpit come from?

One theory:
A cockpit is a hole in the ground (or other enclosed area) where cock's fight (like dog fights).
There was a council chamber at Westminster named "the cockpit," since it was built over the site of one.
A fitting name, since a council chamber is a "control center" where debates are argued and decisions are made.
The "control center" of a plane is therefore called a cockpit? Esp. a dog-fighting airplane?

Those crazy English...