  With the launch of the Chandra X-Ray Observatory and XMM-Newton, X-ray
astronomy has entered an era of precision science. The precision observational
data taken by these satellites require precision basic physics data for their
analysis. The present authors have recently published a series of papers in
which they have reported the results of the accurate calculations of the
electron-ion thermal bremsstrahlung which are particularly suited for the
analysis of the high-temperature galaxy clusters. In this paper we will present
accurate analytic fitting formulae for the nonrelativistic electron-electron
thermal bremsstrahlung Gaunt factor which will be useful for the analysis of
the X-ray observational data taken by the Chandra X-Ray Observatory and
XMM-Newton. With the publication of the present paper X-ray astronomers will be
provided with an accurate thermal bremsstrahlung Gaunt factor which has an
overall accuracy better than 1% for the temperature range 6.0 <log T[K] < 8.5.
