Hydrogen molecules in selected core-nonpenetrating Rydberg-Stark states have been decelerated from a mean initial velocity of 500 m=s to zero velocity in the laboratory frame and loaded into a threedimensional electrostatic trap. Trapping times, measured by pulsed electric field ionization of the trapped molecules, are found to be limited by collisional processes. As Rydberg states can be deexcited to the absolute ground state, the method can be applied to generate cold samples of a wide range of species. DOI: 10.1103/PhysRevLett.103.123001 PACS numbers: 37.10.De, 32.60.+i, 33.80.Rv, 37.20.+j Considerable efforts are being invested in the development of methods to generate translationally cold (<1 K) samples of molecules [1][2][3][4]. These efforts are driven by the desires to study molecular collisions at very low energies [5][6][7], to carry out precision spectroscopic measurements [8,9], and to explore the properties of molecular gases close to quantum degeneracy [2][3][4].Since Although Rydberg-Stark deceleration is in principle applicable to any gas phase species, its application to molecular samples has suffered from two drawbacks: First, the Stark states of nonhydrogenic atoms and molecules undergo avoided crossings for electric field strengths at and beyond the Inglis-Teller limit [32]. At such crossings, low-field-seeking states can be converted to highfield-seeking states limiting the range of usable field strengths to F < 1 3n 5 (in atomic units). Second, whereas the lifetimes of n > 25 Rydberg-Stark states of atoms exceed 50 s, the lifetimes of such states in molecules are generally limited by predissociation and usually much shorter [33]. Both of these drawbacks have their origin in core-penetrating, low-' components of the Stark wave functions and can therefore be overcome simultaneously by eliminating such components using a suitable multiphoton excitation sequence.In the absence of an external electric field, the excitation sequence chosen for H 2raises, at each step, the value of ', J, and jM J j by one. By virtue of the fact that in para-H 2 singlet-triplet mixing is negligible below n ¼ 100 [34], the accessible Rydberg series converging to the N þ ¼ 0 ionic ground state are ' ¼ J ¼ jM J j ¼ 3 Rydberg states. In the presence of a dc electric field at excitation, ' and J are no longer good quantum numbers. However, provided the direction of propagation of the laser beams employed is parallel to PRL 103, 123001 (2009)