The move comes at a time when its bigger rival NSE, which controls a large part of trade volumes in the country, has also initiated a similar process for its chief.
Interestingly, some reports mention that Chauhan is in the race to take over the corner office at NSE.
In an advertisement posted on Tuesday, the 1875-established BSE said it is looking for a results-oriented leader having an experience of 20 years, with the "highest ethical standards".
Stock exchanges have frequently faced troubles over integrity - witnessed through the emergence of scandals.
NSE, which is passing through a scandal involving an ex-chief, is also stressing on governance aspect in its search for a new head.
Understanding of the financial markets, technology and operations are the desired qualities in the candidate, the advertisement said.
A market-savvy leader with an entrepreneurial approach, capable of working in a closely regulated and supervised system, is being sought, it added.
She or he must be having prior experience in managing expectations of diverse stakeholders, including regulators, investors, customers and employees, and should meet Capital markets regulator Sebi's eligibility criteria.
The candidate should hold a post-graduation or master's degree, and the compensation will be as per industry standards, the advertisement noted.
The appointment may be for a period of up to five years, it said, specifying April 23 as the last date for submission of applications.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)