Long flexible rods are considered; these are hard cylindrical particles with a contour length less than their persistence length. We show that an attractive interaction between the rods, with a range of the order of the diameter of the hard core, causes dilute phases of the rods to collapse to a dense phase with a volume fraction of order 0.1. The temperature of this collapse is insensitive to the persistence length; it is significantly lower than that for perfectly rigid rods even for very large persistence lengths.