Is there an advantage to linear chromosomes?
I think it is the wrong question. You assume that eukaryotes developed from a single-cell organism with circular DNA. Then, clearly, there must have been an advantage of (newly) developing a linear genome. But eukaryotes could have developed from an organism with linear DNA, too. There are still a few bacterial species with linear chromosomes, so this is not unlikely. We don't know, however.

On the other hand, if linearisation developed independently, you can learn from bacteria why it might have occurred:

J. N. Volff, J. Altenbuchner: A new beginning with new ends: linearisation of circular chromosomes during bacterial evolution. In: FEMS microbiology letters. 186, 2, May 2000, 143–150, PMID 10802162. (Review).

Abstract:


  Bacterial circular chromosomes have sporadically become linearised
  during prokaryote evolution. Unrelated bacteria, including the
  spirochete Borrelia burgdorferi and the actinomycete Streptomyces,
  have linear chromosomes. Linear chromosomes may have been formed
  through integration of linear plasmids. Linear chromosomes use linear
  plasmid strategies to resolve the 'end-of-replication problem', but
  they have generally retained from their circular ancestors a central
  origin of replication. Streptomyces linear chromosomes are very
  unstable and at high frequency undergo amplifications and large
  deletions, often removing the telomeres. At least in Streptomyces,
  chromosome linearity is reversible: circular chromosomes arise
  spontaneously as products of genetic instability or can be generated
  artificially by targeted recombination. Streptomyces circularised
  chromosomes are very unstable as well, indicating that genetic
  instability is not confined to the linearised chromosomes. Bacterial
  linear chromosomes may contain telomere-linked regions of enhanced
  genomic plasticity, which undergo more frequent genetic exchanges and
  rearrangements and allow differential evolution of genes, depending on
  their chromosomal location.