This paper proposes a method for optimal PMU placement for ambient data-based mode estimation. In contrast to traditional methods for PMU placement where the main objective is to maximize observability of the system, the proposed method uses the critical inter-area mode estimation accuracy as the criterion for siting and ranking PMU locations and signals. The criterion is defined as the critical mode's damping ratio estimation variance. First, this criterion is computed for all signals, and next signal locations are ranked accordingly. Finally, the signal with the lowest criterion value represents the best location for a PMU. Two methods for computing the criterion are presented: 1) Monte Carlo simulation and 2) an approximate expression for the estimation covariance matrix. Furthermore, the paper discusses the possibility of combining two or more synchrophasor signals in order to improve the accuracy of the estimate. The application of the proposed methods is demonstrated using the KTH Nordic 32 test system.