High-resolution (R = 143,000), high signal-to-noise (S/N = 700-1100) Gemini-S bHROS spectra have been analyzed in a search for 6Li in 5 stars which host extrasolar planets. The presence of detectable amounts of 6Li in these mature, solar-type stars is a good monitor of accretion of planetary disk material, or solid bodies themselves, into the outer layers of the parent stars. Detailed profile-fitting of the Li I resonance doublet at lambda 6707.8 A reveals no detectable amounts of 6Li in any star in our sample. The list of stars analyzed includes HD 82943 for which 6Li has been previouly detected at the level of 6Li/7Li = 0.05 +/- 0.02. The typical limits in the derived isotopic fraction are 6Li/7Li <= 0.00-0.02. These upper limits constrain the amount of accreted material to less than ~ 0.02 to 0.5 Jovian masses. The presence of detectable amounts of 6Li would manifest itself as a red asymmetry in the Li I line-profile and the derived upper limits on such asymmetries are discussed in light of three-dimensional hydrodynamic model atmospheres, where convective motions also give rise to slight red asymmetries in line profiles.