Possible Clues:

• India's ___ Chess Academy
• "She's So High" singer Bachman
• Chess champ before and after Botvinnik
• 1960 world chess champ
• He defeated Botvinnik in 1960
• Chess's Mikhail
• 'Que ___?' ('What's up?')
• Grand Master of not quite over average stature?
• 1960s chess master Mikhail
• '¿Que ___?' ('How's it going?' in Spanish)