From "Fun Brisk biz Semyatitsh" by M. Weisman (It doesn't appear to be online yet)
Of the Brisker Rav I do not have the ability to write.
Every Brisker Jew carries the name R Chaim Solovetchik close to his heart and has his own memories of him. My words can certainly make him no greater then he was. All that I could wish to say of him, I will say in these words "May his like increase in Israel."
A most eloquent non-description which however tells us so much.
For a more wordy description, see S.'s great post and the Brisk Sefer Zikaron, Yaakov Mark B'Mechitzasum Shel Gedolei Torah pgs. 36-54, and R' Zevin's classic study of R' Chaim's methodology in Ishim V' Shittos. It is noteworthy that no comprehensive biography of R' Chaim exists to date.