A quasi-periodic transition to chaos has been observed experimentally in counter-rotating Taylor-Couette flow. This scenario occurs when a circular path is followed around a multicritical point in parameter space. (The multicritical point results from the nonlinear interaction between azimuthal wavenumbers m = 2 and m = 3.) To complement the experiments, the reduced amplitude equations that describe this mode interaction have been solved numerically. The numerical solutions follow a transition to chaos similar to the one observed experimentally. Both experimental and numerical chaotic flows are characterized by broadband spectra, low fractal dimension and a positive largest Lyapunov exponent. This result indicates that the chaos observed experimentally might be due to the mode interaction, and that the mathematical model might be appropriate to describe chaotic behavior in real flows.