Bright, ultracompact X-ray binaries observed in dense star clusters, such as Galactic globular clusters, must have formed relatively recently, since their lifetimes as persistent bright sources are short (e.g., ~10^8 yr above 10^36 erg/s for a 1.4 Msun neutron star accreting from a degenerate helium companion with an initial mass of ~0.2 Msun). Therefore, we can use the present conditions in a cluster core to study possible dynamical formation processes for these sources. Here we show that direct physical collisions between neutron stars and red giants can provide a sufficient formation rate to explain the observed numbers of bright sources. These collisions produce tight, eccentric neutron star -- white dwarf binaries that decay to contact by gravitational radiation on timescales ~10^6-10^10 yr, usually shorter and often much shorter than the cluster age.

4 pages, 1 figure, in emulateapj style. ApJ Letters, in press, includes corrections in proofs