We report the first observation of the charmless hyperonic B decay, B+-->LambdaLambdaK+, using a 140 fb(-1) data sample recorded at the Upsilon(4S) resonance with the Belle detector at the KEKB (e+)(e-) collider. The measured branching fraction is B(B+-->LambdaLambdaK+) = (2.91(+0.90)(-0.70) +/- 0.38) x 10(-6). We also perform a search for the related decay mode B+-->LambdaLambdapi+, but do not find a significant signal. We set a 90% confidence-level upper limit of B(B+-->LambdaLambdapi+) < 2.8 x 10(-6).