As told by Mr. K.A. Martin Xavier, Chitosan can not be dissolved without adding acid. I have heard about the water soluble Chitosan which is prepared by hydrolysing Chitosan using hydrogen peroxide.
Acetic acid can alone dissolve Chitosan. I have prepared gel of Chitosan by using 1% acetic acid solution and from that I have made Chitosan beads for my adsorption experiments.
As already told by others. It is difficult to dissolve chitosan in DMSO.
However, regarding to this paper https://www.researchgate.net/publication/244728743_Dissolution_of_Chitosan_in_Dimethyl_Sulfoxide_by_Salt_Formation, some of chitosan salts, such as salicylic acid, can dissolve in DMSO.
Here is protocol from that paper:
Chitosan (NHAc = 0.2, Mn = 24000) dissolved in water in the presence of equimolar of acid listed in Table 1. After freeze drying of aq chitosan salt solution, a part of chitosan-acid salts such as pTsOH, CSA, MeSO3H, and salicylic acid (2-HOC6H4COOH) dissolve in DMSO.
Article Dissolution of Chitosan in Dimethyl Sulfoxide by Salt Formation