We report the field-orientation dependent specific heat of the spin-triplet superconductor Sr2RuO4 under the magnetic field aligned parallel to the RuO2 planes with high accuracy. Below about 0.3 K, striking 4-fold oscillations of the density of states reflecting the superconducting gap structure have been resolved for the first time. We also obtained strong evidence of multi-band superconductivity and concluded that the superconducting gap in the active band, responsible for the superconducting instability, is modulated with a minimum along the [100] direction.PACS numbers: 74.70. Pq,74.25.Bt,74.25.Op,74.25.Dw Since the discovery of its superconductivity [1], the layered ruthenate Sr 2 RuO 4 has attracted a keen interest in the physics community [2]. The superconductivity of Sr 2 RuO 4 has pronounced unconventional features such as: the invariance of the spin susceptibility across its superconducting (SC) transition temperature T c [3,4], appearance of spontaneous internal field [5], evidence for two-component order parameter [6] and absence of a Hebel-Slichter peak [7]. These features are coherently understood in terms of spin-triplet superconductivity with the vector order parameter d(k) =ẑ∆ 0 (k x + ik y ), representing the spin state S z = 0 and the orbital wave function with L z = +1, called a chiral p-wave state.The above vector order parameter leads to the gap1/2 , which is isotropic because of the quasi-two dimensionality of the Fermi surface consisting of three cylindrical sheets [8]. However, a number of experimental results [9,10,11,12,13] revealed the power-law temperature dependence of quasiparticle (QP) excitations, which suggest lines of nodes or nodelike structures in the SC gap. There have been many theoretical attempts (anisotropic p-wave or f-wave states) to resolve this controversy [14,15,16,17,18,19]. Although all these models suggest a substantial gap anisotropy, magnetothermal conductivity measurements with the applied field rotated within the RuO 2 plane down to 0.35 K revealed little anisotropy [20,21]. To explain those experimental facts as well as the mechanism of the spintriplet superconductivity, several theories [22,23], taking the orbital dependent superconductivity (ODS) into account [24], have been proposed. In these models, there are active and passive bands to the superconductivity: the SC instability originates from the active band with a large gap amplitude; pair hopping across active to passive bands leads to a small gap in the passive bands. The gap structure with horizontal lines of nodes [22] or strong in-plane anisotropy [23] in the passive bands was proposed.In order to identify the mechanism of the spin-triplet superconductivity, the determination of the gap structure in the active band is currently of prime importance. The field-orientation dependent specific heat is a direct measure of the QP density of states (DOS) and thus a powerful probe of the SC gap structure [25,26,27,28]. In this Letter, we report high precision experiments of the specific heat as a funct...