The first author conjectured that Chebyshev-type prime bounds hold for Beurling generalized numbers provided that the counting function N(x) of the generalized integers satisfies the L¹ condition
$∫_1^∞ |N(x) - Ax| dx/x^2 < ∞$
for some positive constant A. This conjecture was shown false by an example of Kahane. Here we establish the Chebyshev bounds using the L¹ hypothesis and a second integral condition.