Bicameral

Bicameral is an SAT word, meaning "two chambers" just as you thought it would.

Weird science
It is one of those books that is either complete rubbish or a work of consummate genius; Nothing in between! Probably the former, but I'm hedging my bets. In psychology, "bicameralism" is Julian Jaynes' hypothesis that the left and right sides of the human brain used to operate separately, with the thoughts of one appearing as auditory hallucinations in the other, until just a few thousand years ago, when humans suddenly became conscious as we know it.

Supposedly, one half of the brain thought, and then the other half received messages via auditory hallucinations and obeyed without question, as it was not capable of independent thought.

Jaynes supports his theory by stating that no people in ancient texts such as the Old Testament of the Bible or the Iliad are described as taking part in cognitive processes (which is fairly obvious, since some of the texts are in third-person and/or non-autobiographical) with Ecclesiastes, Psalms, and other later prophets being notable exceptions, and reasoning that people with schizophrenia are remnants of this state of mind.

There are many flaws in his theories, such as the fact that many human populations have been isolated for significantly longer than 3000 years, and yet still all think in the modern sense, and that the Epic of Gilgamesh, the oldest known work of literature, describes Gilgamesh as performing introspection, something that would be impossible under Jaynes' hypothesis.

This idea is not widely accepted and there's some lack of falsifiable versions of the hypothesis, but at least a few psychologists consider the idea "interesting" rather than "crank." It has had a bit of a pop cultural influence regardless of its truth, notably featuring in multiple works by Neal Stephenson including Snow Crash.

Politics
It refers to any legislative house in government which has two independent yet essential chambers. The United States Congress is one such bicameral body, composed of the House of Representatives and the Senate. Other bicameral bodies include the Australian, Canadian, and British parliaments. Many other parliamentary democracies (including Denmark, Finland, New Zealand, and Norway) only have one legislative house, that is, a unicameral system.

Except for those studying for end-of-high-school standardized tests or those studying political science or government courses, there is absolutely no reason to know this word.