We report on the observation of sympathetic cooling of a cloud of fermionic 6 Li atoms which are thermally coupled to evaporatively cooled bosonic 87 Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for BoseEinstein condensation and the Li cloud colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |as| = 20 +9 −6 aB. We found that the presence of residual rubidium atoms in the |2, 1 and the |1, −1 Zeeman substates gives rise to important losses due to inelastic collisions.PACS numbers: 05.30. Fk, 05.30.Jp, 32.80.Pj, The recent realization of degenerate gases of homonuclear diatomic molecules is an important achievement for the physics of ultracold dilute quantum gases [1,2]. The key to this spectacular success was the use of Feshbach resonances which allow for an adiabatic transformation from free pairs to molecules in the least bound state close to the dissociation energy [3]. The large internal energy makes the gas unstable against collisions between the molecules, which transform the energy into kinetic energy of the collision partners [4]. The very long lifetimes of up to several 10 s observed for dimers made of fermionic 6 Li [2] are explained by the fact that the atoms are only loosely bound with a binding energy of 1 µK such that they still behave very much like individual atoms [5]. Collisions are thus suppressed due to Pauli-blocking. Fermionic lithium is now a very promising candidate for exploring the cross-over regime between the Bardeen-Cooper-Schrieffer (BCS) model for superconductivity based on Cooper pairs and the regime of a Bose-Einstein condensate of composite bosons [6].In contrast to homonuclear dimers molecules made of two different atomic species exhibit a permanent electric dipole moment. The LiRb dimer has a very large permanent electric dipole moment of up to 4.2 Debye [7]. The intermolecular interaction in such a heteronuclear gas has a pronounced long-range character, which fundamentally alters its behavior at low temperatures [8] and brings global properties of the gas into play. The geometric shape of the cloud for instance will influence the total interaction energy and thus the stability of the gas [9].A possible approach to generate a polar molecular gas would use a Feshbach resonance in close analogy to the homonuclear experiments [1,2]. Only recently first heteronuclear Feshbach resonances have been observed [10]. Weakly bound heteronuclear molecules are expected to be relatively stable against collisions if one of the two atoms is a fermion [5]. For such molecules Pauli-blocking is at least partially effective, even though reactive collisions may reduce their lifetime [11]. As an alternative to Feshbach resonances, photoassociation is used to transform atomic pairs into molecules. Photoassociation has been extensively investigated for the homonuclear case [12], and there are already examples of successf...