We investigate the relationship between orbital instability and decoherence in de Sitter (dS) spacetime. We consider a simple quadratic toy model proposed by Brandenberger, Laflamme and Miji\ifmmode \acute{c}\else \'{c}\fi{} of two interacting scalar fields in a dS background. It admits a modewise separation, with each mode consisting of a pair of nonautonomous coupled harmonic oscillators. We show that the (classical) maximal Lyapunov exponent of every mode equals the asymptotic rate of (quantum) von Neumann entropy production of each oscillator, assuming an initial vacuum. We find that for moderately long times after horizon crossing, orbital instability, entropy and single-mode squeezing are larger for increasing coupling strength. If the entropy of an oscillator increases more rapidly than squeezing, for example in the strong-coupling regime for not too high frequencies, the noise of every quadrature of the asymptotic state will be larger than the vacuum noise. The results suggest the possibility that simple, nonlinear interacting physical processes with unstable or chaotic classical counterparts may provide an important contribution to the effectiveness of the classicalization of cosmological scalar fields during a dS stage of spacetime expansion.