In order to establish an objective framework for studying galaxy morphology, we have developed a quantitative two-parameter description of galactic structure that maps closely on to Hubble's original tuning fork. Any galaxy can be placed in this "Hubble space", where the x-coordinate measures position along the early-to-late sequence, while the y-coordinate measures in a quantitative way the degree to which the galaxy is barred. The parameters defining Hubble space are sufficiently robust to allow the formation of Hubble's tuning fork to be mapped out to high redshifts. In the present paper, we describe a preliminary investigation of the distribution of local galaxies in Hubble space, based on the CCD imaging atlas of Frei et al. (1996). We find that barred, weakly-barred, and unbarred galaxies are remarkably well-separated on this diagnostic diagram. The spiral sequence is clearly bimodal and indeed approximates a tuning fork: strongly-barred and unbarred spirals do not simply constitute the extrema of a smooth unimodal distribution of bar strength, but rather populate two parallel sequences. Strongly barred galaxies lie on a remarkably tight sequence, strongly suggesting the presence of an underlying unifying physical process. Rather surprisingly, weakly barred systems do not seem to correspond to objects bridging the parameter space between unbarred and strongly barred galaxies, but instead form an extension of the regular spiral sequence. This relation lends support to models in which the bulges of late-type spirals originate from secular processes driven by bars. ; Comment: Accepted for publication in The Astronomical Journal. Figure 2 is too large to be embedded in the paper, and has been included as a JPEG image