We report the observation of a two-dimensional (2D) checkerboard charge density wave (CDW) in the low-dimensional superconductor Ta4Pd3Te16. By determining its CDW properties across the temperature-pressure (T-P) phase diagram and comparing with prototypical CDW materials, we conclude that Ta4Pd3Te16 features: a) an incommensurate CDW with a mixed character of dimensions (Q1D considering its needle-like shape along the b-axis, Q2D as the CDW has checkerboard wavevectors, and 3D because of CDW projections along all three axes); and b) one of the weakest CDWs compared to its superconductivity (SC), i.e. enhanced SC with respect to CDW, suggesting an interesting interplay of the two orders.