The layered ternary compound TaIrTe4 has been predicted to be a type-II Weyl semimetal with only four Weyl points just above the Fermi energy. Performing magnetotransport measurements on this material we find that the resistivity does not saturate for fields up to 70 T and follows a ρ ∼ B 1.5 dependence. Angular-dependent de Haas-van Alphen (dHvA) measurements reveal four distinct frequencies. Analyzing these magnetic quantum oscillations by use of density functional theory (DFT) calculations we establish that in TaIrTe4 the Weyl points are located merely ∼ 40-50 meV above the chemical potential, suggesting that the chemical potential can be tuned into the four Weyl nodes by moderate chemistry or external pressure, maximizing their chiral effects on electronic and magnetotransport properties.A recent conceptual breakthrough in the theory and classification of metals is the discovery of Weyl semimetals [1][2][3]. These semimetals have a topologically nontrivial electronic structure with fermionic Weyl quasiparticles -massless chiral fermions that play as well a fundamental role in quantum field theory and high-energy physics [4]. A consequence is that in Weyl semimetals topologically protected surface states appear in the form of Fermi lines that connect Weyl points (WPs) of opposite chirality, commonly referred to as Fermi arcs.Last year it was discovered that actually two types of Weyl fermions may exist in solids [5]. Weyl semimetals of type-I have a point-like Fermi surface and consequently zero density of states at the energy of WPs [6][7][8][9][10][11][12][13][14][15][16][17][18]. This is very different from Weyl semimetals of type-II [5,19], which have thermodynamic density of states at the energy of Weyl nodes and acquire exotic Fermi surfaces: in type-II systems Weyl nodes appear at touching points between electron and hole pockets. The presence of these very peculiar states is predicted to strongly affect magnetotransport properties of a Weyl semimetal and causes the conduction of electric current only in certain directions in presence of a magnetic field [5,20,21]. In spite of the considerable progress made by theory, only a handful of type-II Weyl semimetals have been identified on the basis of electronic band-structure calculations: WTe 2 , MoTe 2 , Ta 3 S 2 , YbMnBi 2 and, very recently, TaIrTe 4 [5,16,[22][23][24][25].Of interest is in particular the orthorhombic ternary compound TaIrTe 4 as it combines structural simplicity with topological WPs: TaIrTe 4 is a structurally layered material which hosts just four type-II WPs, the minimal number of WPs a system with time-reversal invariance can host [22]. Moreover, the WPs are well separated from each other in momentum space. Such a large momentum-space separation promises a strong impact of the Weyl fermions on the transport properties. Indeed, we present in this Letter magnetotransport and magnetic quantum oscillations studies of TaIrTe 4 that evidence a non-saturating magnetoresistance signaling the presence of Weyl nodes. Analyzing de Haas-van Alp...