The linear carbon chain radical C7H has been detected in the same acetylene-argon discharge in which C8H was recently observed. Fifty rotational transitions, 23 in the ground 2 Pi 1/2 state and 27 in the 2 Pi 3/2 state (37 K higher in energy), were measured. Precise values for the rotational, fine structure, and lambda-doubling constants have been derived which allow calculation of the entire microwave and millimeter-wave spectrum to an accuracy of 0.2 km s-1 or better. With the recent discovery of C8H in space, C7H is an excellent candidate for astronomical detection. To aid future observations, the transition frequencies for the most interesting astronomical lines are tabulated.