Do you think your moods are controlled by your brain chemistry or that your brain chemistry dictates your moods? Do you believe people are born with particular emotional temperaments or that they are primarily shaped by environmental factors?
Isn't the first question...redundant? "Are moods controlled by brains" or "Do brains control moods"? 0_o;
As for the second question, I'd say it's a little of both. If your wiring isn't good, and there's too many or too few neurotransmitters firing between your synapses, then yeah...you'll have problems. You'll be depressed, hyper, nervous, or whatever else depending on the type of imbalance. But that's talking about abnormal psychology and people diagnosed with, for example, clinical depression as cited in the DSM-IV.
For a normal, healthy brain, environment is going to play the far greater role. You get a big promotion...you're happy! Somebody runs over your kitten...you're sad! You're brought up in a very controlling environment...you'll be easily frightened, perhaps afraid to speak out. It's possible that minor aberrations could occur and you "just wake up on the wrong side of the bed" one morning, constantly in a foul mood without any sort of catalyst, but I'd venture to say that brain chemistry would take a backseat to the information being processed by our brains in the forms of our thoughts, dreams, concerns, and observations of the world around us.