The discrepancy between the measured and theoretical production cross section of b quarks at the Fermilab Tevatron can probably be explained by the recently proposed scenario of light gluinos of mass 12-16 GeV and light sbottoms of mass 2-5.5 GeV. In this scenario, we study a related process at the Z pole, Z-->b (b) over tilde (*)(1)(g) over tilde+(b) over tilde(b) over tilde (1)(g) over tilde followed by (g) over tilde -->b (b) over tilde (*)(1)/(b) over tilde(b) over tilde (1). The hadronic branching ratio for this channel is (1-3)x10(-3), which is of the order of the size of the uncertainty in R-b. We find that a typical event consists of an energetic prompt bottom jet back to back with a "fat" bottom jet, which consists of a bottom quark and two bottom squarks. Such events with a 10(-3) branching ratio may affect the measurement of R-b; they are even more interesting if the fat bottom jet can be identified.