We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as ``coagulation instability and regard it as a promising mechanism to concentrate dust particles and assist planetesimal formation in the very early stages of disk evolution. Because of dust-density dependence of collisional coagulation efficiency, dust particles efficiently (inefficiently) grow in a region of positive (negative) dust density perturbations, which lead to a small radial variation of dust sizes and as a result radial velocity perturbations. The resultant velocity perturbations lead to dust concentration and amplify dust density perturbations. This positive feedback makes a disk unstable. The growth timescale of coagulation instability is a few tens of orbital periods even when dust-to-gas mass ratio is of the order of $10^{-3}$. In a protoplanetary disk, radial drift and coagulation of dust particles tend to result in dust depletion. The present instability locally concentrates dust particles even in such a dust-depleted region. The resulting concentration provides preferable sites for dust-gas instabilities to develop, which leads to further concentration. Dust diffusion and aerodynamical feedback tend to stabilize short-wavelength modes, but do not completely suppress the growth of coagulation instability. Therefore, coagulation instability is expected to play an important role in setting up the next stage for other instabilities to further develop toward planetesimal formation, such as streaming instability or secular gravitational instability.
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