Optically clear and elastic conductors are critical for the next generation of fully imperceptible stretchable electronics that are not only optically transparent, but also invisible under typical lighting conditions and reading distances. Such conductors have a central role in a wide range of emerging applications such as wearable computing, soft bioelectronics, and biologically-inspired robotics. Here, we introduce a materials architecture and laser-based microfabrication technique to produce electrically conductive circuitry (sheet resistance = 2.95 Ω/sq; conductivity = 5.65×105 S/m) that are soft, elastic (strain limit > 100%), and optically transparent. The circuitry is composed of a grid-like array of visually imperceptible liquid metal (LM) lines on a clear elastomer. The laser fabrication approach allows for fully imperceptible electronics that have not only high optical transmittance (>85% at 550 nm) but also are invisible under typical lighting conditions and reading distances. This unique combination of properties is enabled by using a direct laser writing technique that results in LM grid patterns with a line width and pitch as small as 4.5 μm and 100 μm, respectively – yielding grid-like wiring on a transparent polydimethylsiloxane (PDMS) elastomer substrate that has adequate conductivity for digital functionality but is also well below the threshold for visual perception. The fabricated LM wiring can be readily interfaced with conventional circuit components (e.g., lead wiring, or LED chips) to enable optically clear digital electronics. The electrical, mechanical, electromechanical, and optomechanical characterization of fabricated LM circuits shows that the high conductivity and transparency are preserved at tensile strains of ~100%.