We probed the first 3AU around tau Ceti and epsilon Eridani with the CHARA array (Mt Wilson, USA) in order to gauge the 2micron excess flux emanating from possible hot dust grains in the debris disks and to also resolve the stellar photospheres. High precision visibility amplitude measurements were performed with the FLUOR single mode fiber instrument and telescope pairs on baselines ranging from 22 to 241m of projected length. The short baseline observations allow us to disentangle the contribution of an extended structure from the photospheric emission, while the long baselines constrain the stellar diameter. We have detected a resolved emission around tau Cet, corresponding to a spatially integrated, fractional excess flux of 0.98 +/- 0.21 x 10^{-2} with respect to the photospheric flux in the K-band. Around eps Eri, our measurements can exclude a fractional excess of greater than 0.6x10^{-2} (3sigma). We interpret the photometric excess around tau Cet as a possible signature of hot grains in the inner debris disk and demonstrate that a faint, physical or background, companion can be safely excluded. In addition, we measured both stellar angular diameters with an unprecedented accuracy: Theta_LD(tau Cet)= 2.015 +/- 0.011 mas and Theta_LD(eps Eri)=2.126 +/- 0.014 mas.
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