Lewis & Short

millēsĭmus (-lensimus), a, um, adj. [mille], the thousandth (class.): millesimam partem vix intellego, Cic. Att. 2, 4, 1; cf.: in millesimo corpore, Cels. 2, 6: inter mille rates tua sit millesima puppis, i. e. ultima, Ov H. 13, 97: usura, one for every thousand monthly, Sen. Ira, 3, 33: pagina, Juv. 7, 100.
In plur.: armillam, ex millesimis Mercurii factam, the thousandth part of gain vowed to Mercury, Petr. 67, 7.
Hence, adv.: millēsĭmum, for the thousandth time: Q pater quartum vel potius millesi mum nihii sapit, Cic. Att. 12, 5, 1.