  LHC searches for fermionic top partners $T$ focus on three decay topologies:
$T\to bW$, $T\to tZ$, and $T\to th$. However, top partners may carry new
conserved quantum numbers that forbid these decays. The simplest possibility is
a conserved parity, under which the top partner is odd and all SM states are
even. In this case, decays of top partners may involve new particle-odd
scalars, leading to signal topologies more commonly associated with
supersymmetry, either with or without R-parity conservation. We study a
simplified model in which this possibility is realized, and estimate the bounds
on the top partner mass in this model implied by LHC searches for
supersymmetry. We find that the bounds can be significantly weaker than in the
conventional top partner decay scenario. For example, if the new parity is
exact, a 500 GeV top partner is allowed as long as the lightest parity-odd
scalar mass is between 325 and 500 GeV. The lower allowed top partner mass
reduces the need for fine-tuning in the Higgs mass parameter, compared to the
conventional decay scenario. We also present an explicit model, the Oddest
Little Higgs, which exhibits this phenomenology.
