Is Chairman Mao's mausoleum near Tienanmen Square?

Yes, the Memorial Hall of Chairman Mao is near the Tiananmen Square.

For your information, to visit the museum, you will need to show your passports to enter and you are not allowed to take anything with you like bag, camera, water etc. Also, you will need to queue up. According to my experience, it may take around 1-2 hours for the queue. Hope the information helps.