Simple theoretical calculations have suggested that small-body impacts onto Pluto's newly discovered small satellites, Nix and Hydra, are capable of generating time-variable rings or dust sheets in the Pluto system. Using Hubble Space Telescope ACS data obtained on 2006 February 15 and 2006 March 2, we find no observational evidence for such a ring system and present the first constraints on the present-day I/F and optical depth of a putative ring system, where I is the observed intensity and πF is the incident (solar) flux. At the 1500 km radial resolution of our search, we place a 3 σ upper limit on the azimuthally averaged normal I/F of ring particles of 5.1 × 10^-7 at a distance of 42,000 km from the Pluto-Charon barycenter, the minimum distance for a dynamically stable ring (Stern et al. 1994; Nagy et al. 2006); 4.4 × 10^-7 at the orbit of Nix; and 2.5 × 10^-7 at the orbit of Hydra. For an assumed ring particle albedo of 0.04 (0.38), these I/F limits translate into 3 σ upper limits on the normal optical depth of macroscopic ring particles of 1.3 × 10^-5 (1.4 × 10^-6), 1.1 × 10^-5 (1.2 × 10^-6), and 6.4 × 10^-6 (6.7 × 10^-7), respectively. Were the New Horizons spacecraft to fly through a ring system with an optical depth of 1.3 × 10^-5, it would collide with a significant number of potentially damaging ring particles. We therefore recommend that, unless tighter constraints can be obtained, New Horizons cross the putative ring plane within 42,000 km of the Pluto-Charon barycenter, where rings are dynamically unstable. We derive a crude estimate of the lifetime of putative ring particles of 900 yr.