We present the first results from our pilot 500 ks Chandra Low Energy Transmission Grating Large Program observation of the soft X-ray brightest source in the z gsim 0.4 sky, the blazar 1ES 1553+113, aimed to secure the first uncontroversial detections of the missing baryons in the X-rays. We identify a total of 11 possible absorption lines, with single-line statistical significances between 2.2σ and 4.1σ. Six of these lines are detected at high single-line statistical significance (3.6 ≤ σ ≤ 4.1), while the remaining five are regarded as marginal detections in association with either other X-ray lines detected at higher significance and/or far-ultraviolet (FUV) signposts. Three of these lines are consistent with metal absorption at z sime 0, and we identify them with Galactic O I and C II. The remaining eight lines may be imprinted by intervening absorbers and are all consistent with being high-ionization counterparts of FUV H I and/or O VI intergalactic medium signposts. In particular, five of these eight possible intervening absorption lines (single-line statistical significances of 4.1σ, 4.1σ, 3.9σ, 3.8σ, and 2.7σ), are identified as C V and C VI Kα absorbers belonging to three WHIM systems at zX = 0.312, zX = 0.237, and langzX rang = 0.133, which also produce broad H I (and O VI for the zX = 0.312 system) absorption in the FUV. For two of these systems (zX = 0.312 and 0.237), the Chandra X-ray data led the a posteriori discovery of physically consistent broad H I associations in the FUV (for the third system the opposite applies), so confirming the power of the X-ray-FUV synergy for WHIM studies. The true statistical significances of these three X-ray absorption systems, after properly accounting for the number of redshift trials, are 5.8σ (zX = 0.312; 6.3σ if the low-significance O V and C V Kβ associations are considered), 3.9σ (zX = 0.237), and 3.8σ (langzX rang = 0.133), respectively.