With reference to the recent developments in science, which one of the following statements is not correct?

The correct answer is: Functional chromosomes can be created by joining segments of DNA taken from cells of different species.

Step-by-Step Explanation and Logical Reasoning:

1. Analyzing the Statement in Option 1:
Chromosomes are complex structures consisting of DNA tightly wrapped around histone proteins, carrying thousands of genes along with specialized structures like centromeres and telomeres. Creating a fully functional artificial chromosome entirely by joining segments of DNA from different species directly is currently not achievable in biotechnology. While recombinant DNA technology allows the splicing of specific gene fragments from different species into vectors (like plasmids), synthesizing functional whole chromosomes from scratch or by joining intact chromosomal segments across different species remains beyond current technological capabilities. Therefore, this statement is not correct.

2. Evaluating Option 2:
"Pieces of artificial functional DNA can be created in laboratories."
This statement is correct. Synthetic biology techniques allow scientists to synthesize custom artificial DNA sequences (gene synthesis) in laboratories, which can perform specific functional roles inside host cells.

3. Evaluating Option 3:
"A piece of DNA taken out from an animal cell can be made to replicate outside a living cell in a laboratory."
This statement is correct. Polymerase Chain Reaction (PCR) is a widely used laboratory technique that enables the amplification and replication of specific DNA segments extracted from living cells in vitro (outside a living cell).

4. Evaluating Option 4:
"Cells taken out from plants and animals can be made to undergo cell division in laboratory petri dishes."
This statement is correct. Cell culture and tissue culture techniques routinely allow plant and animal cells to grow, proliferate, and undergo cell division under controlled laboratory conditions in petri dishes or culture flasks.

Conclusion:
Since the question asks to identify the statement that is not correct, the first statement is the correct choice.