In this paper, we present and analyse optical photometry and spectra of the extremely luminous and slowly evolving Type Ia supernova (SN Ia) 2009dc, and offer evidence that it is a super-Chandrasekhar mass (SC) SN Ia and thus has a SC white dwarf (WD) progenitor. Optical spectra of SN 2007if, a similar object, are also shown. SN 2009dc had one of the most slowly evolving light curves ever observed for a SN Ia, with a rise time of ~23d and {DELTA}m_15_(B)=0.72mag. We calculate a lower limit to the peak bolometric luminosity of ~2.4x10^43^erg/s, though the actual value is likely almost 40 per cent larger. Optical spectra of SN 2009dc and SN 2007if obtained near maximum brightness exhibit strong CII features (indicative of a significant amount of unburned material), and the post-maximum spectra are dominated by iron-group elements (IGEs). All of our spectra of SN 2009dc and SN 2007if also show low expansion velocities. However, we see no strong evidence in SN 2009dc for a velocity `plateau' near maximum light like the one seen in SN 2007if. The high luminosity and low expansion velocities of SN 2009dc lead us to derive a possible WD progenitor mass of more than 2M_{sun} and a 56Ni mass of about 1.4-1.7M{sun}_.