We present Chandra and HST observations of the ultraluminous X-ray source (ULX) IC 342 X-1. The Chandra and HST images are aligned using two X-ray emitting foreground stars. The astrometry corrected position for X-1 is R.A. = 03h45m55.61s, Decl. = +68d04m55.3s (J2000) with an error circle of 0.2". One extended optical source is found in the error circle, which could be the optical counterpart of X-1. The source shows an extended feature in HST images at long wavelengths, which is likely to be a superposition of two point sources, although it is possible that the dimmer one could be a jet. Both sources are much redder than typical for ULX optical counterparts. The brighter one has an absolute magnitude M_V = -5.2 +/- 0.2 and (B-V)_0 = 0.66 +/- 0.13 and the dimmer star is not detected in B and has (B-V)_0 > 2.1. Their colors are consistent with an F8 to G0 Ib supergiant or a carbon star, respectively. However, it is likely that part or most of the optical emission may be due to X-rays reprocessed by the companion star or the accretion disk. The stellar neighborhood of IC 342 X-1 lacks O stars and has a minimum age of ~10 Myr. This excludes the possibility that the surrounding nebula is powered by an energetic explosion of a single massive star that formed a black hole. We suggest that the nebula is most likely powered by an outflow from the X-ray source.