We present data obtained with the Infrared Array Camera (IRAC) aboard the Spitzer Space Telescope (Spitzer) for a sample of 74 young (t < 30 Myr old) Sun-like (0.7 < M(star)/M(Sun) < 1.5) stars. These are a sub-set of the observations that comprise the Spitzer Legacy science program entitled the Formation and Evolution of Planetary Systems (FEPS). Using IRAC we study the fraction of young stars that exhibit 3.6-8.0 micron infrared emission in excess of that expected from the stellar photosphere, as a function of age from 3-30 Myr. The most straightforward interpretation of such excess emission is the presence of hot (300-1000K) dust in the inner regions (< 3 AU) of a circumstellar disk. Five out of the 74 young stars show a strong infrared excess, four of which have estimated ages of 3-10 Myr. While we detect excesses from 5 optically thick disks, and photospheric emission from the remainder of our sample, we do not detect any excess emission from optically thin disks at these wavelengths. We compare our results with accretion disk fractions detected in previous studies, and use the ensemble results to place additional constraints on the dissipation timescales for optically-thick, primordial disks.