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Carbon stars (C>O) were long assumed to all be giants comma because only AGB stars dredge up significant carbon into their atmospheres. We now know that dwarf carbon (dC) stars are actually far more common than C giants. The dCs have accreted C-rich envelope material from an AGB companion comma eventually yielding a white dwarf and a dC that has gained both significant mass and angular momentum. We propose a Chandra study of the nearest known typical dC comma J0435+3401 comma to investigate its extreme X-ray spectral properties and variability comma while using HST to constrain the cooling age of its white dwarf companion. Since dCs are the likely progenitors of CH comma BaII and CEMP stars comma and probably also interacting binaries like CVs comma novae comma or SN Ia comma our results will have wide-ranging implications.