N point vortices with strengths Γᵢ in 2D ideal (Euler) flow obey: Γᵢ ẋᵢ = -∂H/∂yᵢ, Γᵢ ẏᵢ = ∂H/∂xᵢ where the Hamiltonian H = -Σᵢ<ⱼ ΓᵢΓⱼ log|rᵢⱼ| / (2π). This is an exactly integrable system for N≤3 but becomes chaotic for N≥4. The leapfrog motion of two co-rotating vortex pairs is a classic integrable solution. Vortex colors indicate sign: blue = positive circulation, red = negative.