Hello Aspirant.. Fortunately to pursue Graduation in Psychology , it is not mandatory to have psychology as a subject in 10+2 or intermediate. So if you find  Psychology fascinating. you can freely take admission in any College or University which offer B.Sc psychology. Given below are some best Colleges for B.Sc psy in Chennai.

1.Presidency College (Autonomous)-B.Sc & M.Sc Both 

2.Dr Ambedkar Cover Arts College- B.Sc

3.Alagappa Institute Of Technology - B.Sc

4.Ethiraj College for Women ( Autonomous)-B.Sc

5.Stella Maris College- B.Sc

6.Rajaranjan Academy - B.Sc and M.Sc both

7. Women's Christian College- B.Sc, M.Sc & M.Phil

8.Justice Basheer Ahmed Sayaeed women's College (Autonomous)- B.Sc and M.Sc both.

9.St. Thomas College Of Arts And Science-B.Sc

If you are intrested in distance mode education you apply in Tamil Nadu open University which offers B.Sc, M.Sc & Post Graduate Diploma or Annamalia University Distance Education.

Hope it helps.

Good Luck.