The magnetic penetration depth λ as a function of temperature in Bi4O4S3 was studied by muon-spin-spectroscopy measurements. The superfluid density of Bi4O4S3 is found to be very low. The dependence of λ −2 on temperature possibly suggests the existence of two s-wave type energy gaps with the zero-temperature values of 0.93(3) and 0.09(4) meV. The upturn in the temperature dependence of the upper critical field close to Tc further supports multi-gap superconductivity in Bi4O4S3. The presence of two superconducting energy gaps is consistent with theoretical and other experimental studies. However, a single-gap s-wave model fit with a gap of 0.88(2) meV can not be ruled out completely. The value of λ(T ) at T = 0 K is estimated to be λ(0) = 861(17) nm, one of the largest of all known layered superconductors, reflecting a very low superfluid density.PACS numbers: 74.25.Ha, 76.75.+i Recent years have witnessed a growing interest in superconductivity within layered crystal structure compounds. The recent discovery of superconductivity in the BiS 2 -based compound Bi 4 O 4 S 3 [1, 2] with a transition temperature (T c ) of ≈ 4.5 K has further fostered the research interest in layered superconductors. Exotic superconductivity with higher T c and/or with unconventional pairing mechanism has often been found in materials with a layered crystal structure. In this context, the most familiar examples are the high-T c cuprates and the Fe-based superconductors, where the corresponding CuO 2 or Fe 2 An 2 (An = P, As, Se, Te) layer plays an important role in determining the superconducting properties [3][4][5]. Similarly, the BiS 2 layer is believed to be the basic building block for inducing superconductivity in Bi 4 O 4 S 3 and it is expected that the doping mechanism resembles that of cuprates and Fe-based superconductors. This argument is supported by the discovery of other BiS 2 -based superconductors ReO 1−x F x BiS 2 (Re = La, Ce, Pr, and Nd) with T c values of 10.6, 3.0, 5.5, and 5.6 K, respectively [6][7][8][9].Up to now, only very few theoretical and experimental studies have been performed on Bi 4 O 4 S 3 . The parent phase (Bi 6 O 8 S 5 ) is a band insulator which becomes superconducting after electron doping [1]. A first principles band structure calculation indicates that the superconductivity in Bi 4 O 4 S 3 originates from two Bi 6p orbitals, as they intersect the Fermi surface [10]. A RPA analysis of a two-orbital model for the BiS 2 -based superconductors suggests that the spin fluctuations promote competing A 1g and B 2g superconducting states with similar pairing strengths [11]. Transport measurements under pressure reveal that T c of Bi 4 O 4 S 3 decreases monotonically without distinct change of the normal state metallic behavior [12]. The exact nature of the superconducting state is still debated. Hall, Seebeck coefficients, and magnetoresistance measurements suggest exotic multiband features in Bi 4 O 4 S 3 [13]. Recent measurements of the temperature dependence of the magnetic penetration depth λ us...