Trying to determine the complexity of a song by counting the number of chords it contains is a mistake. For example, you sometimes hear people complain about "three-chord rock" and so on. First, it's important to remember that chords are resting places and not starting points. Therefore all music will tend to gravitate towards a small number of chords - often three, because all seven notes of a scale can be harmonized in that manner. Second, chords can be used in all kinds of ways - they can provide energy (dissonance) or rest (consonance). "Beyond Belief", the opening track on Elvis Costello's brilliant Imperial Bedroom album from 1982, is an example of both of these points. Check it out.