Based on Gaia DR2 data and new CHIRON radial velocities, we have discovered that two nearby stellar associations UPK 535 (318.08+/-0.29pc, 25^+15^_-10_Myr, 174 stars) and Yep 3 (339.54+/-0.25pc, 45^+55^_-20_Myr, 297 stars) in the Gum Nebula have recently collided. We project stars' current positions, motions, and measurement uncertainties backward and forward through time in a 10000-trial Monte Carlo simulation. On average, the associations' centres of mass come within 18.89+/-0.73pc of each other 0.84+/-0.03Myr ago. A mode of 54+/-7 close (<1pc) stellar encounters occur during the collision. We cannot predict specific star-star close encounters with our current ~7.6pc distance precision and 21.5-per-cent-complete radial velocity sample. Never the less, we find that two stars in UPK 535 and two stars in Yep 3 undergo a nonspecific close encounter in >70 per cent of trials and multiple close encounters in ~30 per cent. On average, the closest approach of any two stars is 0.13+/-0.06pc, or 27000+/-12000au. With impulse-tracing values up to 2.7^+3.1^_-1.1_(M_{sun}_/pc^2^)/(km/s) , such close encounters could perturb stars' Oort cloud comets (if present), cause heavy bombardment events for exoplanets (if present), and reshape solar system architectures. Finally, an expansion of our simulation suggests other associations in the region are also interacting. Association collisions may be commonplace, at least in the Gum Nebula straddling the Galactic plane, and may spur solar system evolution more than previously recognized.