In 2001, Rima Chacaturian earned a diploma and a special prize for the best performance of Latvian composer's work in the International Young Pianists Competition Jurmala - 2001. In 2002, she won the first prize the international competition - festival "Music Without Limits’’ in Druskininkai. In 2003, became laureate in national J. S. Bach Piano Competition in Vilnius. In 2008, she participated in the international "Nordic Piano Competition” in Malmo (Sweden) and won the First Prize (a Blüthner Model 6 grand piano) and a special prize for the best performance of O. Messiaen work. In 2009, she won I prize in IX Lithuanian Composers’s Chamber Music Competition.
Rima Chacaturian participated in various festivals in Lithuania and Europe –“Summer with piano music” in Druskininkai, “Interpretations of young generation”, “Christopher Summer Festival”. In 2009 she participated in “Birmingham International Piano Academy” in England and in “Academie musicale de Villecroze“ in France.

Rima Chacaturian has played with Jurmala’s and Kaunas chamber orchestras. She had concerts in Germany, Sweden, England, France. Rima Chacaturian participated in masterclasses with famous professors – D.Merlet, P.Donohoe, J.Lowenthal, N. Seriogina, V.Nosina and others.