The Swans' equaliser brushed the hand of the Spanish centre-back on its way towards goal, a strike which cancelled out Danny Graham's opener on his return to the Liberty Stadium
Danny Graham came back to haunt his former club by ending a run of 30 games without a goal, putting the visitors ahead after nine minutes, but the Tigers were pegged back in the second half by a goal that was allowed to stand despite the ball striking Chico's hand.
Hull fashioned the better chances in the closing stages of the match, with a David Meyler goal disallowed for offside, though neither side could find the decisive breakthrough.
Spanish attacker Michu returned from a five-week injury lay-off in one of three changes to Swansea’s side, while goalkeeper Michel Vorm missed out with a recurrence of a knee problem. Curtis Davies, meanwhile, was back from suspension for Hull and replaced Robbie Brady.
Graham struck with the game's first real chance, the Sunderland loanee beating Chico to Ahmed Elmohamady's far-post cross after Ashley Williams had passed the ball straight into the path of the Egyptian.
Swansea dominated possession for much of the first half without creating much in the way of chances as Hull produced yet another stout defensive display. However, defender Ben Davies perhaps should have done better when he fired over from the edge of the area following neat work from the hosts.
Swansea began to exert more pressure in the opening stages of the second half, and were rewarded when Chico levelled; The 26-year-old appeared to turn home Shelvey's left-wing free kick with his arm, but referee Chris Foy allowed the goal to stand.
Goalscorer Graham was replaced by Robert Koren soon after - the ex-Watford man holding his back as he left the field - but Hull continued to create opportunities.
After an appeal for handball in the area against Dwight Tiendalli had gone unanswered, a tight offside call denied Meyler a goal and Gerhard Tremmel then displayed excellent reflexes to deny Yannick Sagbo from distance.
Michu went close for Swansea at the other end, forcing a strong stop from Allan McGregor, but that proved to be the last meaningful chance of a match that ended with a flurry of late bookings as both sides moves up a place in the Premier League table.