We propose a new model of trading in OTC markets. Dealers accumulate inventories by trading with end-investors and trade among each other to reduce their inventory holding costs. Core dealers use a more efficient trading technology than peripheral dealers, who are heterogeneously connected to core dealers and trade with each other bilaterally. Connectedness affects prices and allocations if and only if the peripheral dealers' aggregate inventory position differs from zero. Price dispersion increases in the size of this position. The model generates new predictions about the effects of dealers' connectedness and dealers' aggregate inventories on prices.