This paper studies the taxation of realized capital gains in the decentralized market for private businesses, an asset class with empirically large unrealized capital gains. I develop a dynamic heterogeneous agent model of private business, with incomplete markets, financial frictions, and an over-the-counter market for bilaterally exchanging business productivity levels. By influencing the reservation prices of sellers and buyers, the capital gains tax affects both exchange allocations and exchange asset prices. Quantitative analysis suggests that if financial frictions are severe, then a positive capital gains tax rate maximizes aggregate productivity. Yet the productivity gains stem from a decrease in aggregate input demand, rather than from an increase in aggregate output, which is necessarily lower under any positive tax rate relative to that under a zero tax rate.