We investigate whether Palestinian Arabic (PA), as spoken by the local Palestinian refugee population in Beirut, is converging with Lebanese Arabic (LA), the majority variety. Using a sociolinguistic framework, we target three variables considered to be susceptible to convergent change. We find evidence of contact-induced change in PA in the variable raising of word-medial /a:/ to [e:], as well as in the attrition of socially marked exponents of verbal negation. By contrast, in the case of the third variable, the future temporal reference system, the evidence for convergence is less compelling on account of key differences between the contact varieties, including the vertiginous rise of the proclitic future marker ħa- in PA. We implicate the respective social salience of the targeted variables in their differential susceptibility to convergence. Our results afford new insights into dialect contact and elucidate under-studied patterns of grammatical variation and change in Levantine Arabic.