Methylene Chloride will dissolve PLA well. You can buy it as IPS Weld-on 3 or 4 if you look up the MSDS youll see they are both some percentage methylene chloride. I have used it to weld PLA parts together with great success.
Weld-On 3 = 80-95% Methylene Chloride, 1-15% Dimethyl Glutarate, 1-5% Methyl Methacrylate Monomer
Weld-On 4 = 30-60% Methylene Chloride, 40-60% Trichloroethylene, <1% Methyl Methacrylate Monomer
Ebay seems to be the easiest place to order it online: http://www.ebay.com/sch/IPS%20weld%20on%204