We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in d<3, while in d≥3 there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for n-particle bound states in d dimensions when d+n≥4. Exact calculations of disorder-averaged n-particle Green's functions support our hypothesis. In particular, we show that three-particle states in d=1 with nearest-neighbor repulsion will delocalize with Wc≈1.4t and with localization length critical exponent ν=1.5±0.3. The delocalization transition can be understood by means of a mapping onto a noninteracting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.