Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that, when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ('scarred') along the shortest periodic orbits of a classical particle moving within the confining potential, While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self-retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference.