The scaling behavior near the transition between plateaus of the integer quantum Hall effect has traditionally been interpreted on the basis of a two-parameter renormalization group flow conjectured from the non-linear sigma model of Pruisken. Yet, this scaling picture never led to any analytical understanding of the critical point. Here we propose a novel description of the critical point as Pruisken's nonlinear sigma model coupled to a maximally gauged Wess-Zumino-Witten model of level 4. This proposal explains the existing numerical data for the multifractal scaling exponents of critical wavefunctions.