Your chain may be too long, or your rear derailleur's cage windup spring may need to be tensioned. In the large-to-large gear combination, can you pull down fairly far on the chain, or is it tight across the top and bottom?
By the way, "chain suck" refers to a chain's failure to release from the chainring at the bottom of the pedal stroke; this is not your problem.
What kind of bike is that? With the gear cables routed under the bottom bracket and the plain parallelogram Campag. rear derailleur (Gran Sport?), I am guessing circa 1980.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069