As you want here I am providing Union Bank Of India Tamilnadu Branches info on your demand I am providing same :

IFSC Code: UBIN0533238
Bank: Union Bank Of India
Business Hours: Monday to Saturday 10 am to 4 pm
Mode Of Payment: Cash,Cheque,Demand Draft and Net banking
Branch: Chamiers Road Chennai
Contact:
Bank Details: Union Bank Of India Chamiers Road Chennai UBIN0533238
Remittance Services: NEFT
Location: Chennai, Chennai
City: Chennai
District: Chennai
State: Tamil Nadu
Pincode: 600018
Country: IN
Address: 67, Chamiers Road, Chennai,Tamil Nadu,Pin - 600 018.

IFSC Code: UBIN0533254
Bank: Union Bank Of India
Business Hours: Monday to Saturday 10 am to 4 pm
Mode Of Payment: Cash,Cheque,Demand Draft and Net banking
Branch: Mount Road Chennai
Contact:
Bank Details: Union Bank Of India Mount Road Chennai UBIN0533254
Remittance Services: NEFT
Location: Chennai, Chennai
City: Chennai
District: Chennai
State: Tamil Nadu
Pincode: 600002
Country: IN
Address: 152, Mount Road,Madras, Tamil Nadu,Pin - 600 002.

IFSC Code: UBIN0533262
Bank: Union Bank Of India
Business Hours: Monday to Saturday 10 am to 4 pm
Mode Of Payment: Cash,Cheque,Demand Draft and Net banking
Branch: Chennai Main
Contact:
Bank Details: Union Bank Of India Chennai Main UBIN0533262
Remittance Services: NEFT
Location: Chennai, Chennai
City: Chennai
District: Chennai
State: Tamil Nadu
Pincode: 600108
Country: IN
Address: 139, Broadway, P.B. No. 1931,Chennai, Tamil Nadu,Pin - 600 108.

IFSC Code: UBIN0533289
Bank: Union Bank Of India
Business Hours: Monday to Saturday 10 am to 4 pm
Mode Of Payment: Cash,Cheque,Demand Draft and Net banking
Branch: Kathivakkam (Ennore)
Contact:
Bank Details: Union Bank Of India Kathivakkam (Ennore) UBIN0533289
Remittance Services: NEFT
Location: Chennai, Chennai
City: Chennai
District: Chennai
State: Tamil Nadu
Pincode: 600057
Country: IN
Address: Kathivakkam Municipal Complexshop No:44 Ennore

IFSC Code: UBIN0533297
Bank: Union Bank Of India
Business Hours: Monday to Saturday 10 am to 4 pm
Mode Of Payment: Cash,Cheque,Demand Draft and Net banking
Branch: Madhavaram
Contact:
Bank Details: Union Bank Of India Madhavaram UBIN0533297
Remittance Services: NEFT
Location: Chengai Anna, Chennai
City: Chengai Anna
District: Chennai
State: Tamil Nadu
Pincode: 600110
Country: IN
Address: 1, G. N. T. Road, Moolakadai,Madras, Dist. Chengai Anna,Tamil Nadu, Pin - 600 110.


For more info about Union Bank Of India branches in Chennai I am giving process here:

Go on the Union Bank Of India official website

Click on branch & ATM locator which is under show button given at the right hand side

By click there you will move on branch locator page which look like given below image