We report muon-spin-rotation (@SR) measurements of the a-b magnetic penetration depth (k,b) in the vortex state of high quality single crystals of YBa2Cu306.95. Contrary to earlier pSR studies on powders and crystal mosaies, 1/)j.,b shows a strong linear temperature dependence below 50 K which weakens with increasing magnetic field. These results support recent microwave cavity measurements in zero field and provide further evidence for unconventional pairing of carriers. PACS numbers: 74.25.Bt, 74.25.Ha, 76.75.+i Considerable debate has arisen over the nature of the electronic ground state in high-T, superconductors such as YBazCu30q s. Although pairing of charge carriers is almost certainly involved, the underlying symmetry of the pairing state (s wave, d wave, or other) has been the subject of a long and continuing controversy. Measurements of the temperature dependence of the magnetic penetration depth (A, ) are one way to probe the nature of the low energy excitations and the pairing state. In a simple London model, 1 4&nse m~c2 where n, is the superfluid density and m* is the eA'ective mass of the carriers. Early muon-spin-rotation (pSR) studies on sintered powders and lower quality crystals of YBazCu307 t; have concluded that I/k has a weak temperature dependence for T«T"suggesting there is an energy gap in the spectrum of excitations [I], as expected for conventional s-wave pairing. However, other techniques such as NMR [2] and infrared reflectance [3] failed to provide clear evidence for such a gap. Many of these latter experiments can be explained if there are nodes in the superconducting energy gap function, t)q, as predicted by some theories in which short range repulsive interactions play a dominant role in the pairing mechanism [4]. Recent microwave cavity perturbation measurements on high quality YBa2Cu30695 crystals have found a linear temperature dependence in k below 30 K [5], consistent with line nodes in A1, expected from singlet d"2 -r2 wave pairing [6]. Similar studies of thin films of YBa2Cu307 -q and Bi2Sr2CaCu208 have shown a quadratic increase in A, (T) [7]. It has been proposed that the differences are due to impurity scattering, which result in a crossover from linear to quadratic behavior in a d-wave superconductor [8].Although the microwave method has high precision, it is not sensitive to the absolute value of X,b(0), only to changes in k,h, as a function of temperature, and this only within the microwave skin depth of the surface. Consequently, such measurements leave some ambiguity as to the behavior of I/A, and thus n, Mu. on spin rotation, on the other hand, gives a direct measure of the magnetic field distribution and A, ,b (the penetration depth in the ab plane) in the bulk of the sample. In this Letter we present @SR measurements of I/X, b in high quality single crystals of YBazCu30b95 similar to those used in the microwave cavity perturbation studies [5]. Although );b(T=0) is close to that determined from earlier @SR studies on sintered powders and crystal mosaics, the t...