Observations of ultraluminous infrared galaxies (ULIRGs) with an achieved r
esolution approaching the diffraction limit in the mid-infrared from 8 to 2
5 mu m using the Keck Telescopes are reported. We find extremely compact st
ructures, with spatial scales of less than 0 ".3 (diameter) in six of the s
even ULIRGs observed. These compact sources emit between 30% and 100% of th
e mid-infrared energy from these galaxies. We have utilized the compact mid
-infrared structures as a diagnostic of whether an AGN or a compact (100-30
0 pc) starburst is the primary power source in these ULIRGs. In Markarian 2
31, the upper limit on the diameter of the 12.5 mu m source, 0 ".13, shows
that the size of the infrared source must increase with increasing waveleng
th, consistent with AGN models. In IRAS 05189-2524 and IRAS 08572+3915 ther
e is strong evidence that the source size increases with increasing wavelen
gth. This suggests heating by a central source rather than an extended lumi
nosity source, consistent with the optical classification as an AGN. The co
mpact mid-infrared sources seen in the other galaxies cannot be used to dis
tinguish the ultimate luminosity source. If these ULIRGs are powered by com
pact starbursts, the star formation rates seen in the central few hundred p
arsecs far exceed the global rates seen in nearby starburst galaxies, and a
pproach the surface brightness of individual clusters in nearby starburst g
alaxies.