Although hunting for chaos is not as popular as it used to be, we dedicate this paper to the presentation of a new strange attractor. It concerns the most important dynamic process in our life, that is the emergence and evolution of love in interpresonal relationships. More precisely, we show that a romantic relationship can be unpredictable - chaotic - on the sole basis of the interplay of the characters involved. To do this, we analyse the celebrated triangular love story described in Jules et Jim, a novel by Henri-Pierre Roché, using a mathematical model. As in physics and biology, the theory of coupled oscillators proves to be a powerful tool in identifying minor but strategically important factors - here jealousy and complaisance - as sources of unpredictability. Our results also highlight the genius of François Truffaut, whose film - one of the masterpieces on love and friendship - is based on the novel. Truffaut successfully reproduced the turbulence of the feelings and the uncertainty over their future by systematically exploiting the metaphor of stretching and folding, both visually and in the scripts, and especially with the song "Le tourbillon de la vie" - a beautiful hymn to chaos. And all this was done in 1961, two years before the publication of Lorenz's paper!