  We performed a signature-based search for long-lived charged massive
particles (CHAMPs) produced in 1.0 $\rm{fb}^{-1}$ of $\bar{p}p$ collisions at
$\sqrt{s}=1.96$ TeV, collected with the CDF II detector using a high
transverse-momentum ($p_T$) muon trigger. The search used time-of-flight to
isolate slowly moving, high-$p_T$ particles. One event passed our selection
cuts with an expected background of $1.9 \pm 0.2$ events. We set an upper bound
on the production cross section, and, interpreting this result within the
context of a stable scalar top quark model, set a lower limit on the particle
mass of 249 GeV/$c^2$ at 95% C.L.
