There is a body of work to suggest that there is brain lateralisation for emotional processing. There is a convincing review here. http://www.ncbi.nlm.nih.gov/pubmed/15886400.
Unfortunately there does not seem to be open access to the whole paper. However, from the abstract you will glean that the lateralisation is complex, there is not a claim that either the right or a left hemisphere does emotion. There is also some interesting neuroscience investigations that show an EEG asymmetry between the right and left hemisphere that depends on the valence ( positive or negative) of the emotional experience. http://www.sciencedirect.com/science/article/pii/S0301051109001823
Again the lateralisation effect is complex and has involved some research trying to tease out dispositional and state factors.
Obviously a stable evidence outcome from this work is important since emotion and cognition are so entangled!