Giant star formation clumps in dwarf irregular galaxies can have masses exceeding a few percent of the galaxy mass enclosed inside their orbital radii. They can produce sufficient torques on dark matter halo particles, halo stars, and the surrounding disk to lose their angular momentum and spiral into the central region in 1Gyr. Pairs of giant clumps with similarly large relative masses can interact and exchange angular momentum to the same degree. The result of this angular momentum loss is a growing central concentration of old stars, gas, and star formation that can produce a long-lived starburst in the inner region, identified with the blue compact dwarf (BCD) phase. This central concentration is proposed to be analogous to the bulge in a young spiral galaxy. Observations of star complexes in five local BCDs confirm the relatively large clump masses that are expected for this process. The observed clumps also seem to contain old field stars, even after background light subtraction, in which case the clumps may be long-lived. The two examples with clumps closest to the center have the largest relative clump masses and the greatest contributions from old stars. An additional indication that the dense central regions of BCDs are like bulges is the high ratio of the inner disk scale height to the scale length, which is comparable to1for four of the galaxies. © 2012 The American Astronomical Society. All rights reserved.