We report the detection of comet 67P/Churyumov-Gerasimenkos dust trail and nucleus in 24 micron Spitzer Space Telescope images taken February 2004. The dust trail is not found in optical Palomar images taken June 2003. Both the optical and infrared images show a distinct neck-line tail structure, offset from the projected orbit of the comet. We compare our observations to simulated images using a Monte Carlo approach and a dynamical model for comet dust. We estimate the trail to be at least one orbit old (6.6 years) and consist of particles of size >~100 micron. The neck-line is composed of similar sized particles, particles of size but younger in age. Together, our observations and simulations suggest grains 100 micron and larger in size dominate the total mass ejected from the comet. The radiometric effective radius of the nucleus is 1.87 +/- 0.08 km, derived from the Spitzer observation. The Rosetta spacecraft is expected to arrive at and orbit this comet in 2014. Assuming the trail is comprised solely of 1 mm radius grains, we compute a low probability (~10^-3) of a trail grain impacting with Rosetta during approach and orbit insertion.